相关论文: Model of the $p$-Adic Random Walk in a Potential

This article introduces a model for interacting vertex-reinforced random walks, each taking values on a complete sub-graph of a locally finite undirected graph. The transition probability for a walk to a given vertex depends on the…

We consider the random walk of a particle in a two-dimensional self-affine random potential of Hurst exponent $H=1/2$ in the presence of an external force $F$. We present numerical results on the statistics of first-passage times that…

We introduce a persistent random walk model for the stochastic transport of particles involving self-reinforcement and a rest state with Mittag-Leffler distributed residence times. The model involves a system of hyperbolic partial…

The motion of self-propelled particles is modeled as a persistent random walk. An analytical framework is developed that allows the derivation of exact expressions for the time evolution of arbitrary moments of the persistent walk's…

The L\'evy walk process with rests is discussed. The jumping time is governed by an $\alpha$-stable distribution with $\alpha>1$ while a waiting time distribution is Poissonian and involves a position-dependent rate which reflects a…

We derive the characteristic function of stochastic functionals of a random walk whose position is reset to the origin at random times drawn from a general probability distribution. We analyze the long-time behavior and obtain the temporal…

We study the transition probability, say $p_A^n(x,y)$, of a one-dimensional random walk on the integer lattice killed when entering into a non-empty finite set $A$. The random walk is assumed to be irreducible and have zero mean and a…

Random walk has wide applications in many fields, such as machine learning, biology, physics, and chemistry. Random walk can be discrete or continuous in time and space. Asymmetric random walk could be described by drift-diffusion equation.…

Equation for anomalous diffusion in momentum space, recently obtained in the recent paper (S.A. Trigger, ArXiv 0907.2793 v1, [cond-matt. stat.-mech.], 16 July 2009) is solved for the stationary and non-stationary cases on basis of the…

We consider random walks in Dirichlet environment (RWDE) on $\Z ^d$, for $ d \geq 3 $, in the sub-ballistic case. We associate to any parameter $ (\alpha_1, ..., \alpha_{2d}) $ of the Dirichlet law a time-change to accelerate the walk. We…

The Dirac equation can be modelled as a quantum walk, with the quantum walk being: discrete in time and space (i.e. a unitary evolution of the wave-function of a particle on a lattice); homogeneous (i.e. translation-invariant and…

We analyse how simple local constraints in two dimensions lead a defect to exhibit robust, non-transient, and tunable, subdiffusion. We uncover a rich dynamical phenomenology realised in ice- and dimer-type models. On the microscopic scale…

The behavior of the maximal displacement of a supercritical branching random walk has been a subject of intense studies for a long time. But only recently the case of time-inhomogeneous branching has gained focus. The contribution of this…

In this paper we consider a generalization of analysis on $p$-adic numbers field to the $m$ case of $m$-adic numbers ring. The basic statements, theorems and formulas of $p$-adic analysis can be used for the case of $m$-adic analysis…

We consider the continuous-time random walk of a particle in a two-dimensional self-affine quenched random potential of Hurst exponent $H>0$. The corresponding master equation is studied via the strong disorder renormalization procedure…

A comprehensive convergence and stability analysis of some probabilistic numerical methods designed to solve Cauchy-type inverse problems is performed in this study. Such inverse problems aim at solving an elliptic partial differential…

We give a complete and unified description -- under some stability assumptions -- of the functional scaling limits associated with some persistent random walks for which the recurrent or transient type is studied in [1]. As a result, we…

In this paper we present an integro-differential diffusion equation for continuous time random walk that is valid for a generic waiting time probability density function. Using this equation we also study diffusion behaviors for a couple of…

Cauchy's formula was originally established for random straight paths crossing a body $B \subset \mathbb{R}^{n}$ and basically relates the average chord length through $B$ to the ratio between the volume and the surface of the body itself.…

Motivated by various recent experimental findings, we propose a dynamical model of intermittently self-propelled particles: active particles that recurrently switch between two modes of motion, namely an active run-state and a turn state,…