相关论文: One step beyond: The excursion set approach with c…

The recent realization of a "Levy glass" (a three-dimensional optical material with a Levy distribution of scattering lengths) has motivated us to analyze its one-dimensional analogue: A linear chain of barriers with independent spacings s…

People organize in groups and contagions spread across them. A simple stochastic process, yet complex to model due to dynamical correlations within and between groups. Moreover, groups can evolve if agents join or leave in response to…

We consider two models of one-dimensional random walks among biased i.i.d. random conductances: the first is the classical exponential tilt of the conductances, while the second comes from the effect of adding an external field to a random…

This paper presents a new derivation of the Generalized Poisson distribution. This distribution provides a good fit to the evolved, counts-in-cells distribution measured in numerical simulations of hierarchical clustering from Poisson…

A known limitation of time-dependent mean-field approaches is a lack of quantum tunneling for collective motions such as in sub-barrier fusion reactions. As a first step toward a solution, a time-dependent model is considered using a…

The problem of a restricted random walk on graphs which keeps track of the number of immediate reversal steps is considered by using a transfer matrix formulation. A closed-form expression is obtained for the generating function of the…

We consider the partially asymmetric simple exclusion process (PASEP) when its steady-state probability distribution function can be written in terms of a linear superposition of product measures with a finite number of shocks. In this case…

We present a closed-form expression for the survival probability of a biased random walker to first reach a target site on a 1D lattice. The expression holds for any step number $N$ and is computationally faster than non-closed-form results…

A particle subject to successive, random displacements is said to execute a random walk (in position or some other coordinate). The mathematical properties of random walks have been very thoroughly investigated, and the model is used in…

We compute the posterior distributions of the initial population and parameter of binary branching processes, in the limit of a large number of generations. We compare this Bayesian procedure with a more na\"ive one, based on hitting times…

We study how the order of N independent random walks in one dimension evolves with time. Our focus is statistical properties of the inversion number m, defined as the number of pairs that are out of sort with respect to the initial…

We consider the branching random walk on the real line where the underlying motion is of a simple random walk and branching is at least binary and at most decaying exponentially in law. It is well known that the normalized empirical measure…

Let $X_1$, $X_2$, $...$ be a sequence of independently and identically distributed random variables with $\mathsf{E}X_1=0$, and let $S_0=0$ and $S_t=S_{t-1}+X_t$, $t=1,2,...$, be a random walk. Denote $\tau={cases}\inf\{t>1: S_t\leq0\},…

We identify a fundamental phenomenon of heterogeneous one dimensional random walks: the escape (traversal) time is maximized when the heterogeneity in transition probabilities forms a pyramid-like potential barrier. This barrier corresponds…

We investigate searching efficiency of different kinds of random walk on complex networks which rely on local information and one-step memory. For the studied navigation strategies we obtained theoretical and numerical values for the graph…

We revise the encounter-based approach to imperfect diffusion-controlled reactions, which employs the statistics of encounters between a diffusing particle and the reactive region to implement surface reactions. We extend this approach to…

We investigate the first-passage properties of bursty random walks on a finite one-dimensional interval of length L, in which unit-length steps to the left occur with probability close to one, while steps of length b to the right --…

In this article, we study branching random walks on graphs modeling division-mutation processes inspired by adaptive immunity. We apply the theory of expander graphs on mutation rules in evolutionary processes and obtain estimates for the…

Exploiting the coherent medium approximation, random walk among sites distributed randomly in space is investigated when the jump rate depends on the distance between two adjacent sites. In one dimension, it is shown that when the jump rate…

An initial screening experiment may lead to ambiguous conclusions regarding the factors which are active in explaining the variation of an outcome variable: thus adding follow-up runs becomes necessary. We propose a fully Bayes objective…