相关论文: Quenched exit estimates and ballisticity condition…

We consider a mortal random walker on a family of hierarchical graphs in the presence of some trap sites. The configuration comprising the graph, the starting point of the walk, and the locations of the trap sites is taken to be exactly…

We consider a model, introduced by Boldrighini, Minlos and Pellegrinotti, of random walks in dynamical random environments on the integer lattice Z^d with d>=1. In this model, the environment changes over time in a Markovian manner,…

We investigate random walks in independent, identically distributed random sceneries under the assumption that the scenery variables satisfy Cramer's condition. We prove moderate deviation principles in dimensions two and larger, covering…

Quantum walks with long-range steps $R^{-\gamma}$ ($R$ being the distance between sites) on a discrete line behave in similar ways for all $\gamma\geq2$. This is in contrast to classical random walks, which for $\gamma >3$ belong to a…

In this paper, we establish a quenched invariance principle for the random walk on a certain class of infinite, aperiodic, oriented random planar graphs called "T-graphs" [Kenyon-Sheffield04]. These graphs appear, together with the…

The parametric maximum likelihood estimation problem is addressed in the context of quantum walk theory for quantum walks on the lattice of integers. A coin action is presented, with the real parameter $\theta$ to be estimated identified…

We consider a branching random walk in a random space-time environment of disasters where each particle is killed when meeting a disaster. This extends the model of the "random walk in a disastrous random environment" introduced by [15]. We…

We study high moments of truncated Wigner nxn random matrices by using their representation as the sums over the set W of weighted even closed walks. We construct the subset W' of W such that the corresponding sum diverges in the limit of…

We study the 2-dimensional uniform prudent self-avoiding walk, which assigns equal probability to all nearest-neighbor self-avoiding paths of a fixed length that respect the prudent condition, namely, the path cannot take any step in the…

One can define a random walk on a hypercubic lattice in a space of integer dimension $D$. For such a process formulas can be derived that express the probability of certain events, such as the chance of returning to the origin after a given…

The analysis of a physical problem simplifies considerably when one uses a suitable coordinate system. We apply this approach to the discrete-time quantum walks with coins given by $2j+1$-dimensional Wigner rotation matrices (Wigner walks),…

Unlike classical simple random walks, one-dimensional random walks in random environments (RWRE) are known to have a wide array of potential limiting distributions. Under certain assumptions, however, it is known that CLT-like limiting…

We study simple random walk on the class of random planar maps which can be encoded by a two-dimensional random walk with i.i.d. increments or a two-dimensional Brownian motion via a "mating-of-trees" type bijection. This class includes the…

Rotor walk is deterministic counterpart of random walk on graphs. We study that under a certain initial configuration in Z^d, n particles perform rotor walks from the origin consecutively. They would stop if they hit the origin or infinity.…

In this paper, we study random walks evolving on Z in a dynamic random environment that we assume to have time correlations that decrease polynomially fast. We show a law of large numbers by generalizing methods already used for the…

For a random walk in a uniformly elliptic and i.i.d. environment on $\mathbb Z^d$ with $d \geq 4$, we show that the quenched and annealed large deviations rate functions agree on any compact set contained in the boundary $\partial…

Let $\{Z_n\}_{n\geq 0 }$ be a $d$-dimensional supercritical branching random walk started from the origin. Write $Z_n(S)$ for the number of particles located in a set $S\subset\mathbb{R}^d$ at time $n$. Denote by…

We study biased random walk on the infinite connected component of supercritical percolation on the integer lattice $\mathbb{Z}^d$ for $d\geq 2$. For this model, Fribergh and Hammond showed the existence of an exponent $\gamma$ such that:…

Random walks of n steps taken into independent uniformly random directions in a d-dimensional Euclidean space (d larger than 1), are named Dirichlet when their step lengths are distributed according to a Dirichlet law. The latter continuous…

Place an obstacle with probability $1-p$ independently at each vertex of $\mathbb Z^d$, and run a simple random walk until hitting one of the obstacles. For $d\geq 2$ and $p$ strictly above the critical threshold for site percolation, we…