arXiv 1202.56432012-02math.PR

Quenched large deviations for multidimensional random walk in random environment with holding times

Ryoki Fukushima, Naoki Kubota

备注：: This is the corrected version of the paper. 24 pages
发表信息：: Journal of Theoretical Probability, 27(4), pp.1140-1166, 2014
DOI：: 10.1007/s10959-013-0514-z

英文摘要：

We consider a random walk in random environment with random holding times, that is, the random walk jumping to one of its nearest neighbors with some transition probability after a random holding time. Both the transition probabilities and the laws of the holding times are randomly distributed over the integer lattice. Our main result is a quenched large deviation principle for the position of the random walk. The rate function is given by the Legendre transform of the so-called Lyapunov exponents for the Laplace transform of the first passage time. By using this representation, we derive some asymptotics of the rate function in some special cases.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Quenched large deviations for multidimensional random walk in random environment: a variational formula

We take the point of view of the particle in a multidimensional nearest neighbor random walk in random environment (RWRE). We prove a quenched large deviation principle and derive a variational formula for the quenched rate function. Most of the previous results in this area rely on the subadditive ergodic theorem. We employ a different technique which is based on a minimax theorem. Large deviation principles for RWRE have been proven for i.i.d. nestling environments subject to a moment condition and for ergodic uniformly elliptic environments. We assume only that the environment is ergodic an…

2008-04-09math.PR

Quenched invariance principle for multidimensional ballistic random walk in a random environment with a forbidden direction

We consider a ballistic random walk in an i.i.d. random environment that does not allow retreating in a certain fixed direction. We prove an invariance principle (functional central limit theorem) under almost every fixed environment. The assumptions are nonnestling, at least two spatial dimensions, and a $2+ε$ moment for the step of the walk uniformly in the environment. The main point behind the invariance principle is that the quenched mean of the walk behaves subdiffusively.

2007-03-27math.PR

Limiting distributions and large deviations for random walks in random environments

This thesis concerns the study of random walks in random environments (RWRE). Since there are two levels of randomness for random walks in random environments, there are two different distributions for the random walk that can be studied. The quenched distribution is the law of the random walk conditioned on a given environment. The annealed distribution is the quenched law averaged over all environments. The main results of the thesis fall into two categories: quenched limiting distributions for one-dimensional, transient RWRE and annealed large deviations for multidimensional RWRE. The analy…

2008-10-01math.PR

Multidimensional Random Polymers : A Renewal Approach

In these lecture notes, which are based on the mini-course given at 2013 Prague School on Mathematical Statistical Physics, we discuss ballistic phase of quenched and annealed stretched polymers in random environment on ${\mathbb Z}^d$ with an emphasis on the natural renormalized renewal structures which appear in such models. In the ballistic regime an irreducible decomposition of typical polymers leads to an effectiverandom walk reinterpretation of the latter. In the annealed casethe Ornstein-Zernike theory based on this approach paves the way to an essentially complete control on the level …

2014-11-30cond-mat.stat-mechmath-phmath.MP

Almost sure functional central limit theorem for ballistic random walk in random environment

We consider a multidimensional random walk in a product random environment with bounded steps, transience in some spatial direction, and high enough moments on the regeneration time. We prove an invariance principle, or functional central limit theorem, under almost every environment for the diffusively scaled centered walk. The main point behind the invariance principle is that the quenched mean of the walk behaves subdiffusively.

2008-02-15math.PR

Independent Particles in a Dynamical Random Environment

We study the motion of independent particles in a dynamical random environment on the integer lattice. The environment has a product distribution. For the multidimensional case, we characterize the class of spatially ergodic invariant measures. These invariant distributions are mixtures of inhomogeneous Poisson product measures that depend on the past of the environment. We also investigate the correlations in this measure. For dimensions one and two, we prove convergence to equilibrium from spatially ergodic initial distributions. In the one-dimensional situation we study fluctuations of the …

2018-09-19math.PR

更多相关论文收起更多论文

Continuity result for the rate function of the simple random walk on supercritical percolation clusters

We consider the simple random walk on supercritical percolation clusters in the multidimensional cubic lattice. In this model, a quenched large deviation principle holds for the position of the random walk. Its rate function depends on the law of the percolation configuration, and the aim of this paper is to study the continuity of the rate function in the law. To do this, it is useful that the rate function is expressed by the so-called Lyapunov exponent, which is the asymptotic cost paid by the random walk for traveling in a landscape of percolation configurations. In this context, we first …

2019-08-17math.PR

Large deviations for the local times of a random walk among random conductances in a growing box

We derive an annealed large deviation principle (LDP) for the normalised and rescaled local times of a continuous-time random walk among random conductances (RWRC) in a time-dependent, growing box in $\Z^d$. We work in the interesting case that the conductances are positive, but may assume arbitrarily small values. Thus, the underlying picture of the principle is a joint strategy of small conductance values and large holding times of the walk. The speed and the rate function of our principle are explicit in terms of the lower tails of the conductance distribution as well as the time-dependent …

2013-08-21math.PR

带权重的遍历定理及其在随机测度、RW 均质化和点过程上的 IPS 流体动力学中的应用

An ergodic theorem with weights and applications to random measures, RW homogenization and IPS hydrodynamics on point processes

本文证明了带加权平均的多维遍历定理，并将其应用于随机测度及点过程上随机游走的淬火均质化，移除了原有技术假设，进而确立了对称简单排他过程淬火流体动力学极限的持续有效性。

2024-11-16math-phmath.APmath.MP