Correlated Random Walk Research Articles

Some problems on a one-dimensional correlated random walk with various types of barrier

In this paper one-dimensional correlated random walks (CRW) with various types of barrier such as elastic barriers, absorbing barriers and so on are defined, and explicit expressions are derived for the ultimate absorbing probability and expected duration. Some numerical examples to illustrate the effects of correlation are also presented.

Some Problems on a One-Dimensional Correlated Random Walk with Various Types of Barrier

In this paper one-dimensional correlated random walks (CRW) with various types of barrier such as elastic barriers, absorbing barriers and so on are defined, and explicit expressions are derived for the ultimate absorbing probability and expected duration. Some numerical examples to illustrate the effects of correlation are also presented.

Correlated random walks with random hopping rates

A concentration c of particles undergo correlated random walks on a lattice. The random walks are constrained by only allowing the lattice sites to be singly occupied. This leads to the particles being 'dynamically' correlated. In addition to the dynamic correlations the hopping rates of the particles are disordered. The random hopping rates give rise to 'static' correlations. The resultant model is a many-body problem with disorder. Of principal interest are the new correlations that arise between a disordered random walk and a correlated random walk (CRW) and the effect these correlations have on the self-diffusion constant. The CRW is represented by a nonlinear master equation from which the diffusion constant is obtained by means of classical many-body Green functions. The dynamic correlations are represented by a two-particle Green function. The disorder is studied by means of the bond coherent potential approximation (BCPA). The disorder gives rise to a vertex correction to the two-particle Green function. The vertex correction is obtained by using the BCPA.

Some explicit results for correlated random walks

In a correlated random walk (CRW) the probabilities of movement in the positive and negative direction are given by the transition probabilities of a Markov chain. The walk can be represented as a Markov chain if we use a bivariate state space, with the location of the particle and the direction of movement as the two variables. In this paper we derive explicit results for the following characteristics of the walk directly from its transition probability matrix: (i) n -step transition probabilities for the unrestricted CRW, (ii) equilibrium distribution for the CRW restricted on one side, and (iii) equilibrium distribution and first-passage characteristics for the CRW restricted on both sides (i.e., with finite state space).

Some explicit results for correlated random walks

In a correlated random walk (CRW) the probabilities of movement in the positive and negative direction are given by the transition probabilities of a Markov chain. The walk can be represented as a Markov chain if we use a bivariate state space, with the location of the particle and the direction of movement as the two variables. In this paper we derive explicit results for the following characteristics of the walk directly from its transition probability matrix: (i) n -step transition probabilities for the unrestricted CRW, (ii) equilibrium distribution for the CRW restricted on one side, and (iii) equilibrium distribution and first-passage characteristics for the CRW restricted on both sides (i.e., with finite state space).

Correlated random walks with stay

A random walk describes the movement of a particle in discrete time, with the direction and the distance traversed in one step being governed by a probability distribution. In a correlated random walk (CRW) the movement follows a Markov chain and induces correlation in the state of the walk at various epochs. Then, the walk can be modelled as a bivariate Markov chain with the location of the particle and the direction of movement as the two variables. In such random walks, normally, the particle is not allowed to stay at one location from one step to the next. In this paper we derive explicit results for the following characteristics of the CRW when it is allowed to stay at the same location, directly from its transition probability matrix: (i) equilibrium solution and the fast passage probabilities for the CRW restricted on one side, and (ii) equilibrium solution and first passage characteristics for the CRW restricted on bath sides (i.e., with finite state space).