On the Temporal Order of First-Passage Times in One-Dimensional Lattice Random Walks
نویسنده
چکیده
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 modified Bessel functions of the first kind. By using several transformations simpler integrals are obtained from which for two and three particles asymptotic approximations are derived for large values of the parameters. Expressions of the probability for n particles are also derived. I returned and saw under the sun, that the race is not to the swift, nor the battle to the strong, neither yet bread to the wise, nor yet riches to men of understanding, nor yet favour to men of skill; but time and chance happeneth to them all. George Orwell, Politics and the English Language, Selected Essays, Penguin Books, 1957. (The citation is from Ecclesiastes 9:11.) 2000 Mathematics Subject Classification: 41A60, 60G50, 33C10.
منابع مشابه
Random walks and Brownian motion: a method of computation for first-passage times and related quantities in confined geometries.
In this paper we present a computation of the mean first-passage times both for a random walk in a discrete bounded lattice, between a starting site and a target site, and for a Brownian motion in a bounded domain, where the target is a sphere. In both cases, we also discuss the case of two targets, including splitting probabilities and conditional mean first-passage times. In addition, we stud...
متن کاملA PRELUDE TO THE THEORY OF RANDOM WALKS IN RANDOM ENVIRONMENTS
A random walk on a lattice is one of the most fundamental models in probability theory. When the random walk is inhomogenous and its inhomogeniety comes from an ergodic stationary process, the walk is called a random walk in a random environment (RWRE). The basic questions such as the law of large numbers (LLN), the central limit theorem (CLT), and the large deviation principle (LDP) are ...
متن کاملA path integral formula with applications to quantum random walks in
We consider general quantum random walks in a d-dimensional half-space. We first obtain a path integral formula for general quantum random walks in a d-dimensional space. Our path integral formula is valid for general quantum random walks on Cayley graphs as well. Then the path integral formula is applied to obtain the scaling limit of the exit distribution, the expectation of exit time and the...
متن کاملRandom walks on the Sierpinski Gasket
The generating functions for random walks on the Sierpinski gasket are computed. For closed walks, we investigate the dependence of these functions on location and the bare hopping parameter. They are continuous on the infinite gasket but not differentiable. J. Physique 47 (1986) 1663-1669 OCTOBRE 1986, Classification Physics Abstracts 05.40 05.50 1. Preliminaries and review of known results. C...
متن کاملMean first-passage and residence times of random walks on asymmetric disordered chains
The problems of the first-passage time (FPT) [1, 2] and the residence time (RT) [3] are very important issues in random walk theory. Moreover, several properties of diffusion and transport in disordered systems are based in this concepts. Here, we do not want to present a survey of the enormous literature in the field of mean firstpassage time (MFPT) and mean residence time (MRT) of random walk...
متن کامل