Related papers: Finite Size Effect in Persistence
Let $S$ be the random walk obtained from "coin turning" with some sequence $\{p_n\}_{n\ge 1}$, as introduced in [6]. In this paper we investigate the scaling limits of $S$ in the spirit of the classical Donsker invariance principle, both…
Consider a stochastic process that behaves as a $d$-dimensional simple and symmetric random walk, except that, with a certain fixed probability, at each step, it chooses instead to jump to a given site with probability proportional to the…
Expressions for scaling limits of random walks, such as those obtained in several areas of the Probability theory literature, are of great significance in characterizing long term, stationary behavior of random processes. Presumably, in the…
We investigate the equilibration of a small isolated quantum system by means of its matrix of asymptotic transition probabilities in a preferential basis. The trace of this matrix is shown to measure the degree of equilibration of the…
The equation which describes a particle diffusing in a logarithmic potential arises in diverse physical problems such as momentum diffusion of atoms in optical traps, condensation processes, and denaturation of DNA molecules. A detailed…
A random walk problem with particles on discrete double infinite linear grids is discussed. The model is based on the work of Montroll and others. A probability connected with the problem is given in the form of integrals containing…
A detailed investigation of the scaling properties of the fully finite ${\cal O}(n)$ systems with long-range interaction, decaying algebraically with the interparticle distance $r$ like $r^{-d-\sigma}$, below their upper critical dimension…
The exact solution of directed self-avoiding walks confined to a slit of finite width and interacting with the walls of the slit via an attractive potential has been calculated recently. The walks can be considered to model the…
Exponential, and not Gaussian, decay of probability density functions was studied by Laplace in the context of his analysis of errors. Such Laplace propagators for the diffusive motion of single particles in disordered media were recently…
In a continuous time random walk (CTRW), each random jump follows a random waiting time. CTRW scaling limits are time-changed processes that model anomalous diffusion. The outer process describes particle jumps, and the non-Markovian inner…
We investigate a tight binding quantum walk on a graph. Repeated stroboscopic measurements of the position of the particle yield a measured "trajectory", and a combination of classical and quantum mechanical properties for the walk are…
We consider a Branching Random Walk on $\R$ whose step size decreases by a fixed factor, $0<b<1$, with each turn. This process generates a random probability measure on $\R$, that is, the limit of uniform distribution among the $2^n$…
We consider a class of inhomogeneous media known as composite media that is often encountered in experimental sciences and investigate the persistence probability of a random walker in such a system. Analytical and numerical results for the…
* ACTIVATED RANDOM WALK MODEL * This is a conservative particle system on the lattice, with a Markovian continuous-time evolution. Active particles perform random walks without interaction, and they may as well change their state to…
In the presence of attraction, the jamming transition of packings of frictionless particles corresponds to the rigidity percolation. When the range of attraction is long, the distribution of the size of rigid clusters, $P(s)$, is continuous…
Rare trajectories of stochastic systems are important to understand -- because of their potential impact. However, their properties are by definition difficult to sample directly. Population dynamics provides a numerical tool allowing their…
Finite size scaling for a first order phase transition where a continuous symmetry is broken is developed using an approximation of Gaussian probability distributions with a phenomenological "degeneracy" factor included. Predictions are…
Finite-size scaling arguments naturally lead us to introduce a coordinate-dependent diffusion coefficient in a Fokker-Planck description of the late stage dynamics of unbiased polymer translocation through a membrane pore. The solution for…
Self-similar dynamical processes are characterized by a growing length scale $\xi$ which increases with time as $\xi \sim t^{1/z}$, where z is the dynamical exponent. The best known example is a simple random walk with z=2. Usually such…
We study the long-time behavior of the probability density associated with the decoupled continuous-time random walk which is characterized by a superheavy-tailed distribution of waiting times. It is shown that if the random walk is…