Limit Laws Research Articles

Community Assistance in Understanding the Marriage Age Limit Law

Changes in the minimum age for marriage regulated in Law Number 16 of 2019 have significantly impacted the number of applications for marriage dispensation in North Sulawesi. This service aims to carry out educational activities so that the public understands Law Number 16 of 2019 concerning Marriage Limits. Metode pengabdian ini menggunakan Participatory Rural Appraisal (PRA) atau pendekatan partisipatif, meliputi pelatihan, pendampingan, dan kolaborasi dengan pemangku kepentingan terkait. Implementasinya dimulai dari koordinasi, sosialisasi kegiatan, tahap pelaksanaan kegiatan, keberlanjutan program, penyusunan laporan, hingga monitoring dan evaluasi. The result of this service is that the socialization runs smoothly with a team that expands the target of this socialization to include teenagers, namely students and parents of teenage children. The efforts made by the service team are to provide an understanding of the impacts of underage marriage. This is very important to do considering the condition of society, where child marriages are increasing day by day.

A logical limit law for $231$-avoiding permutations

We prove that the class of 231-avoiding permutations satisfies a logical limit law, i.e. that for any first-order sentence $\Psi$, in the language of two total orders, the probability $p_{n,\Psi}$ that a uniform random 231-avoiding permutation of size $n$ satisfies $\Psi$ admits a limit as $n$ is large. Moreover, we establish two further results about the behavior and value of $p_{n,\Psi}$: (i) it is either bounded away from $0$, or decays exponentially fast; (ii) the set of possible limits is dense in $[0,1]$. Our tools come mainly from analytic combinatorics and singularity analysis.

A note on the Greek Law of Limitation

A note on the Greek Law of Limitation

A limit law for the most favorite point of simplerandom walk on a regular tree

A limit law for the most favorite point of simplerandom walk on a regular tree

Bursts of coalescence within population pedigrees whenever big families occur.

We consider a simple diploid population-genetic model with potentially high variability of offspring numbers among individuals. Specifically, against a backdrop of Wright-Fisher reproduction and no selection, there is an additional probability that a big family occurs, meaning that a pair of individuals has a number of offspring on the order of the population size. We study how the pedigree of the population generated under this model affects the ancestral genetic process of a sample of size two at a single autosomal locus without recombination. Our population model is of the type for which multiple-merger coalescent processes have been described. We prove that the conditional distribution of the pairwise coalescence time given the random pedigree converges to a limit law as the population size tends to infinity. This limit law may or may not be the usual exponential distribution of the Kingman coalescent, depending on the frequency of big families. But because it includes the number and times of big families, it differs from the usual multiple-merger coalescent models. The usual multiple-merger coalescent models are seen as describing the ancestral process marginal to, or averaging over, the pedigree. In the limiting ancestral process conditional on the pedigree, the intervals between big families can be modeled using the Kingman coalescent but each big family causes a discrete jump in the probability of coalescence. Analogous results should hold for larger samples and other population models. We illustrate these results with simulations and additional analysis, highlighting their implications for inference and understanding of multilocus data.

On card guessing with two types of cards

We consider a card guessing strategy for a stack of cards with two different types of cards, say m1 cards of type red (heart or diamond) and m2 cards of type black (clubs or spades). Given a deck of M=m1+m2 cards, we propose a refined counting of the number of correct colour guesses, when the guesser is provided with complete information, in other words, when the numbers m1 and m2 and the colour of each drawn card are known. We decompose the correct guessed cards into three different types by taking into account the probability of making a correct guess, and provide joint distributional results for the underlying random variables as well as joint limit laws.

Bank Resolution and Fundamental Rights – A view from Strasbourg

Abstract This article summarises and puts into context the limited but important case law of the European Court of Human Rights concerning bank resolution procedures, in particular under Article 6 (the right to a fair trial before an independent and impartial tribunal established by law) and Article 1 of the First Protocol (the right of property), as well as the important issue of who has standing under Article 34 to bring proceedings in the name or on behalf of an affected affected bank, its (former) management, share holders, bond holders, creditors or others affected.

Stable laws for random dynamical systems

Abstract In this paper, we consider random dynamical systems formed by concatenating maps acting on the unit interval $[0,1]$ in an independent and identically distributed (i.i.d.) fashion. Considered as a stationary Markov process, the random dynamical system possesses a unique stationary measure $\nu $ . We consider a class of non-square-integrable observables $\phi $ , mostly of form $\phi (x)=d(x,x_0)^{-{1}/{\alpha }}$ , where $x_0$ is a non-recurrent point (in particular a non-periodic point) satisfying some other genericity conditions and, more generally, regularly varying observables with index $\alpha \in (0,2)$ . The two types of maps we concatenate are a class of piecewise $C^2$ expanding maps and a class of intermittent maps possessing an indifferent fixed point at the origin. Under conditions on the dynamics and $\alpha $ , we establish Poisson limit laws, convergence of scaled Birkhoff sums to a stable limit law, and functional stable limit laws in both the annealed and quenched case. The scaling constants for the limit laws for almost every quenched realization are the same as those of the annealed case and determined by $\nu $ . This is in contrast to the scalings in quenched central limit theorems where the centering constants depend in a critical way upon the realization and are not the same for almost every realization.

New National and International Processes of Human Dimensions of the Environmental Rights

Due to activities such as illegal deforestation, production of chemicals and plastics, exploitation of fossil fuels, and other large-scale extractive activities, businesses operating in the global economy routinely compromise human rights to have a healthy, clean, and sustainable environment. This human right was recognized by the United Nations Human Rights Council in 2021 and it includes fundamental rights related to clean air, safe climate, access to safe water and adequate sanitation, healthy and sustainable food production, informal environments for living and working, studying and playing, and biodiversity and a healthy ecosystem. By jeopardizing this human right related to nature, life, health, livelihood, and sustainable development, business activists threaten the life prospects of billions of people. The most vulnerable beneficiaries affected by commercial activities such as children, women, indigenous peoples, local communities, farmers, people with disabilities, and especially those whose identity exists in multiple vulnerable groups usually face the most difficult barriers, including financial, language, information barriers, social labeling associated with human rights violations, lack of access to legal representation, and corruption of law enforcement officials, to adopt effective solutions. When victims in countries with limited law enforcement and economic capacity face corruption and other weaknesses in the rule of law, and when justice must be served through transnational legal actions that are beyond the capacity of most human rights victims, solutions effectively are particularly elusive.

Director's Accountability for the Company's Sales Results and Commissioner's Actions in Asset Recovery

This study examines directors’ accountability for company sales results and commissioners’ actions in asset recovery regarding an embezzlement case involving Conti Chandra, a Director at PT. Bangun Mega Semesta (BMS) in Hotel Batam City Condotel (BCC). Relevant court decisions include Supreme Court Decision No. 567K/PID/2016, Pekanbaru High Court Decision No. 212/Pid.B/2015, and Batam District Court Decision No. 321/Pid.B/2015. It focuses on two main issues: corporate managers’ accountability based on Law No. 40 of 2007 on limited liability companies and criminal liability for “embezzlement crime in position” within a limited liability company. The study uses a normative legal research method with a descriptive approach, relying on secondary data and qualitative analysis. Findings indicate corporate managers’ accountability during general meetings of shareholders. Criminal liability for embezzlement relates to directors’ fiduciary duty to shareholders, requiring prudence, responsibility, and good faith. Two recommendations are proposed: First, The Indonesian government should revise the limited liability company law on holding directors and commissioners accountable for neglecting management and supervision duties and emphasizing fiduciary duty. Second, the Directors of Batam City Condotel should adhere to fiduciary duty principles under the board of commissioners’ supervision.
 Keywords: commissioners actions, directors, embezzlement

On level line fluctuations of SOS surfaces above a wall

Abstract We study the low-temperature $(2+1)$ D solid-on-solid model on with zero boundary conditions and nonnegative heights (a floor at height $0$ ). Caputo et al. (2016) established that this random surface typically admits either $\mathfrak h $ or $\mathfrak h+1$ many nested macroscopic level line loops $\{\mathcal L_i\}_{i\geq 0}$ for an explicit $\mathfrak h\asymp \log L$ , and its top loop $\mathcal L_0$ has cube-root fluctuations: For example, if $\rho (x)$ is the vertical displacement of $\mathcal L_0$ from the bottom boundary point $(x,0)$ , then $\max \rho (x) = L^{1/3+o(1)}$ over . It is believed that rescaling $\rho $ by $L^{1/3}$ and $I_0$ by $L^{2/3}$ would yield a limit law of a diffusion on $[-1,1]$ . However, no nontrivial lower bound was known on $\rho (x)$ for a fixed $x\in I_0$ (e.g., $x=\frac L2$ ), let alone on $\min \rho (x)$ in $I_0$ , to complement the bound on $\max \rho (x)$ . Here, we show a lower bound of the predicted order $L^{1/3}$ : For every $\epsilon>0$ , there exists $\delta>0$ such that $\min _{x\in I_0} \rho (x) \geq \delta L^{1/3}$ with probability at least $1-\epsilon $ . The proof relies on the Ornstein–Zernike machinery due to Campanino–Ioffe–Velenik and a result of Ioffe, Shlosman and Toninelli (2015) that rules out pinning in Ising polymers with modified interactions along the boundary. En route, we refine the latter result into a Brownian excursion limit law, which may be of independent interest. We further show that in a $ K L^{2/3}\times K L^{2/3}$ box with boundary conditions $\mathfrak h-1,\mathfrak h,\mathfrak h,\mathfrak h$ (i.e., $\mathfrak h-1$ on the bottom side and $\mathfrak h$ elsewhere), the limit of $\rho (x)$ as $K,L\to \infty $ is a Ferrari–Spohn diffusion.

Application of fused graphical lasso to statistical inference for multiple sparse precision matrices.

In this paper, the fused graphical lasso (FGL) method is used to estimate multiple precision matrices from multiple populations simultaneously. The lasso penalty in the FGL model is a restraint on sparsity of precision matrices, and a moderate penalty on the two precision matrices from distinct groups restrains the similar structure across multiple groups. In high-dimensional settings, an oracle inequality is provided for FGL estimators, which is necessary to establish the central limit law. We not only focus on point estimation of a precision matrix, but also work on hypothesis testing for a linear combination of the entries of multiple precision matrices. We apply a de-biasing technology, which is used to obtain a new consistent estimator with known distribution for implementing the statistical inference, and extend the statistical inference problem to multiple populations. The corresponding de-biasing FGL estimator and its asymptotic theory are provided. A simulation study and an application of the diffuse large B-cell lymphoma data show that the proposed test works well in high-dimensional situation.

Asymptotic expansions relating to the distribution of the length of longest increasing subsequences

Abstract We study the distribution of the length of longest increasing subsequences in random permutations of n integers as n grows large and establish an asymptotic expansion in powers of $n^{-1/3}$ . Whilst the limit law was already shown by Baik, Deift and Johansson to be the GUE Tracy–Widom distribution F, we find explicit analytic expressions of the first few finite-size correction terms as linear combinations of higher order derivatives of F with rational polynomial coefficients. Our proof replaces Johansson’s de-Poissonization, which is based on monotonicity as a Tauberian condition, by analytic de-Poissonization of Jacquet and Szpankowski, which is based on growth conditions in the complex plane; it is subject to a tameness hypothesis concerning complex zeros of the analytically continued Poissonized length distribution. In a preparatory step an expansion of the hard-to-soft edge transition law of LUE is studied, which is lifted to an expansion of the Poissonized length distribution for large intensities. Finally, expansions of Stirling-type approximations and of the expected value and variance of the length distribution are given.

Critical Analysis of Dowry Culture Through the Lens of Dowry-related Laws and Policies in Pakistan

Dowry, a stark reality, still haunts the larger part of Pakistani society. Whenever a marriage takes place, the burden to provide dowry falls upon the shoulders of the bride’s parents. This particular study aims to critically evaluate the laws and policies made by the Pakistani state to curb the menace of dowry culture. The qualitative method with a particular focus on descriptive and explorative analysis was used to explore and describe the intricate issue at hand. For this, various national and international surveys, reports along scholarly articles were thoroughly analyzed to find out the underlying causes and their consequences. Until now, not only limited laws have been enacted to deal with dowry as a criminal offense but also enforcing mechanisms have been absent for the existing laws. The findings of this study implore the adoption of dowry-related laws with efficient rules of business for the sake of effective implementation.

Governing green open space in indonesia: barriers and opportunities to enhancing enviromental quality

This article discusses the enhancing of governing green open space in Indonesia. It began by looking at the current condition of green open space in Indonesia, highlighting the barriers faced in governing these areas, looking at opportunities to enhancing, and making recommendations to improve green open space governance. Literature review on governance frameworks that can maximize the potential of green open spaces in Indonesia. The results of this study show that there are several constraints in governing green open spaces, including less awareness and understanding among stakeholders, limited funding and resources, inadequate urban planning, limited community involvement, limited law enforcement and monitoring, urbanization and land scarcity, and weak coordination among government agencies in their management bodies. Our findings point to opportunities in governing greenspace areas, by learning from successful projects, exploring global good practices; innovative financing and partnerships; integrating greenspace into urban planning for cohesive neighborhoods; engaging communities for long-term success and shared responsibility; raising awareness of the value of greenspace through educational campaigns; and utilizing technology for data-driven decision-making and community participation. These opportunities contribute to policy recommendations that can be used by the central government and local governments to improve green open space governance in Indonesia.

Two-step nucleation and crystal growth in a metastable solution

This study is concerned with a theory of two-step nucleation and growth of crystals in a metastable liquid. This mechanism is that crystalline nuclei formation occurs in dense liquid clusters suspended in the solution. These clusters contain higher solution concentration and viscosity, leading to a lower surface free energy barrier and faster phase transition route. The theory is based on growth laws of crystals during the two-step bulk phase transformation. At the initial stage, the crystals evolve in a diffusion-limited environment with almost unchanged supersaturation. At the second stage, they become larger, move beyond these clusters, and evolve in accordance with a hyperbolic tangent law. A generalized particle growth law joining the first and second stages is obtained by stitching the diffusion limited and hyperbolic tangent laws. On this basis, an integrodifferential model of the evolution of a polydisperse ensemble of crystals was formulated and solved. The crystal-size distribution function increases and the solution supersaturation remains practically unchanged until the particle size corresponds to a transition in the particle growth rate from a diffusion-limited branch to a hyperbolic tangent branch. This is followed by an increase in the crystal growth rate, a decrease in the distribution function and solution supersaturation. Then the distribution function increases up to the maximum size of crystals grown in the solution. A sufficiently long time interval of almost constant supersaturation and the N-shaped behavior of the distribution function are the consequences of a two-step nucleation and growth mechanisms.

Massachusetts' opioid limit law associated with a reduction in postoperative opioid duration among orthopedic patients.

Postoperative orthopedic patients are a high-risk group for receiving long-duration, large-dosage opioid prescriptions. Rigorous evaluation of state opioid duration limit laws, enacted throughout the country in response to the opioid overdose epidemic, is lacking among this high-risk group. We took advantage of Massachusetts' early implementation of a 2016 7-day-limit law that occurred before other statewide or plan-wide policies took effect and used commercial insurance claims from 2014-2017 to study its association with postoperative opioid prescriptions greater than 7 days' duration among Massachusetts orthopedic patients relative to a New Hampshire control group. Our sample included 14 097 commercially insured, opioid-naive adults aged 18 years and older undergoing elective orthopedic procedures. We found that the Massachusetts 7-day limit was associated with an immediate 4.23 percentage point absolute reduction (95% CI, 8.12 to 0.33 percentage points) and a 33.27% relative reduction (95% CI, 55.36% to 11.19%) in the percentage of initial fills greater than 7 days in the Massachusetts relative to the control group. Seven-day-limit laws may be an important state-level tool to mitigate longer duration prescribing to high-risk postoperative populations.

On finite algebras with probability limit laws

An algebraic system has a probability limit law if the values of terms with independent identically distributed random variables have probability distributions that tend to a certain limit (the limit law) as the number of variables in a term grows. For algebraic systems on finite sets, it is shown that, under some geometric conditions on the set of term value distributions, the existence of a limit law strongly restricts the set of possible operations in the algebraic system. In particular, a system that has a limit law without zero components necessarily consists of quasigroup operations (with arbitrary arity), while the limit law is necessarily uniform. Sufficient conditions are also proved for a system to have a probability limit law, which partly match the necessary ones.

On the distribution of partial quotients of reduced fractions with fixed denominator

In this paper, we study distributional properties of the sequence of partial quotients in the continued fraction expansion of fractions a / N a/N , where N N is fixed and a a runs through the set of mod N N residue classes which are coprime with N N . Our methods cover statistics such as the sum of partial quotients, the maximal partial quotient, the empirical distribution of partial quotients, Dedekind sums, and much more. We prove a sharp concentration inequality for the sum of partial quotients, and sharp tail estimates for the maximal partial quotient and for Dedekind sums, all matching the tail behavior in the limit laws which are known under an extra averaging over the set of possible denominators N N . We show that the distribution of partial quotients of reduced fractions with fixed denominator gives a very good fit to the Gauß–Kuzmin distribution. As corollaries we establish the existence of reduced fractions with a small sum of partial quotients resp. a small maximal partial quotient.

THE FREEDOM OF OPINION EXPRESSION THROUGH SOCIAL MEDIA AND THE IMPACT OF ACTS OF DEFAMATION TO THE PERPETRATOR

<p>This study aims to conduct a juridical review of Article 27 Paragraph (3) of Law Number 11 of 2008 concerning Information and Electronic Transactions relating to freedom of expression and acts of defamation through social media. This study uses a normative legal research method with a literature study approach. The effectiveness of Article 27 Paragraph (3) of Law Number 11 of 2008 in protecting freedom of opinion and overcoming acts of defamation through social media is still limited. Some of the obstacles faced include unclear regulations, limited law enforcement capacity in dealing with cases of defamation on social media, and problems in gathering legal and acceptable electronic evidence in court. Several recommendations to increase the effectiveness of Article 27 Paragraph (3) in overcoming acts of defamation through social media are; further clarification regarding the provisions of Article 27 Paragraph (3) ITE so can be interpreted clearly and do not leave room for different interpretations, increasing the capacity of law enforcement, regulations regarding the collection of electronic evidence that is valid and admissible in court needs to be clarified, wider outreach to the public regarding the risks and legal consequences of acts of defamation through social media and periodic evaluation of the implementation of Article 27 Paragraph (3) of ITE in dealing with defamation cases through social media. Therefore, continuous efforts are needed to increase understanding, awareness, and law enforcement regarding Article 27 Paragraph (3) in overcoming acts of defamation through social media so that freedom of expression can be exercised in a balanced way by avoiding actions that violate the law</p>