Abstract
The Laplace distribution of random processes was observed in numerous situations that include glasses, colloidal suspensions, live cells, and firm growth. Its origin is not so trivial as in the case of Gaussian distribution, supported by the central limit theorem. Sums of Laplace distributed random variables are not Laplace distributed. We discovered a new mechanism leading to the Laplace distribution of observable values. This mechanism changes the contribution ratio between a jump and a continuous parts of random processes. Our concept uses properties of Bernstein functions and subordinators connected with them.
Highlights
Based on a myriad of examples in the physical sciences, 1963 Nobel Prize winner in physicsH.P
As an example for detecting the Laplace confinement in experimental data, we present our analysis of random trajectories obtained from a recent single-particle tracking (SPT) study on G protein-coupled receptors, namely the motion and interaction of individual receptors and G proteins on the surface of living cells [44]
If the pure subdiffusion is characterized by multiple trapping events with infinite mean sojourn time, and the power function exponent of mean-squared displacement (MSD) is constant in time, a truncated power-law distribution of trapping times leads to tempered subdiffusion, in which diffusion is anomalous at short times and normal at long times [45]
Summary
Based on a myriad of examples in the physical sciences, 1963 Nobel Prize winner in physics. It should be noticed that a large part of well-known anomalous diffusion processes can be represented as time-changed Brownian motion. We find that an anomalous diffusion process is represented as time-changed Brownian motion if and only if it is a semimartingale, [33]. It is interesting that the model has a one-to-one connection with the well-known tempered subdiffusion which demonstrates the transition from subdiffusion to normal diffusion in condensed matter physics [54] and geophysics [55], respectively. The subdiffusive dynamics is fruitfully modeled as a diffusive motion X (τ ) subordinated by a wide class of random processes subject to infinitely divisible distributions. Similar analysis of two different forms of the Fokker–Planck equation where the memory kernels are conjugate pairs has been done in [72,73].
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