相关论文: Some results on regularity and monotonicity of the…

We study random walks on the integers driven by a sample of time-dependent nearest-neighbor conductances that are bounded but are permitted to vanish over time intervals of positive Lebesgue-length. Assuming only ergodicity of the…

We construct, for each real number $0\leq \alpha \leq 1$, a random walk on a finitely generated semigroup whose speed exponent is $\alpha$. We further show that the speed function of a random walk on a finitely generated semigroup can be…

In recent years, there has been an interest in deriving certain important probabilistic results as consequences of deterministic ones; see for instance \cite{beig} and \cite{acc}. In this work, we continue on this path by deducing a well…

We consider a simple random walk W_i in 1 or 2 dimensions, in which the walker may choose to stand still for a limited time. The time horizon is n, the maximum consecutive time steps which can be spent standing still is m_n and the goal is…

We prove that for a random walk on the real line whose increments have zero mean and are either integer-valued or spread out (i.e. the distributions of the steps of the walk are eventually non-singular), the Markov chain of overshoots above…

We study analytically a simple random walk model on a one-dimensional lattice, where at each time step the walker resets to the maximum of the already visited positions (to the rightmost visited site) with a probability $r$, and with…

Commonly, normal diffusive behavior is characterized by a linear dependence of the second central moment on time, $< x^2(t) >\propto t$, while anomalous behavior is expected to show a different time dependence, $ < x^2(t) > \propto…

We introduce a Gibbs measure on nearest-neighbour paths of length $t$ in the Euclidean $d$-dimensional lattice, where each path is penalised by a factor proportional to the size of its boundary and an inverse temperature $\beta$. We prove…

We give new criteria for ballistic behavior of random walks in random environment which are perturbations of the simple symmetric random walk on $\mathbb Z^d$ in dimensions $d\ge 4$. Our results extend those of Sznitman [Ann. Probab. 31,…

We show that random walk in uniformly elliptic i.i.d. environment in dimension $\geq5$ has at most one non zero limiting velocity. In particular this proves a law of large numbers in the distributionally symmetric case and establishes…

Let $(X,d)$ be a geodesic Gromov-hyperbolic space, $o \in X$ a basepoint and $\mu$ a countably supported non-elementary probability measure on $\operatorname{Isom}(X)$. Denote by $z_n$ the random walk on $X$ driven by the probability…

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…

We study variable-speed random walks on $\mathbb Z$ driven by a family of nearest-neighbor time-dependent random conductances $\{a_t(x,x+1)\colon x\in\mathbb Z, t\ge0\}$ whose law is assumed invariant and ergodic under space-time shifts. We…

We prove that every random walk in i.i.d. environment in dimension greater than or equal to 2 that has an almost sure positive speed in a certain direction, an annealed invariance principle and some mild integrability condition for…

Consider the dynamic environment governed by a Poissonian field of independent particles evolving as simple random walks on $\mathbb{Z}^d$. The random walk on random walks model refers to a particular stochastic process on $\mathbb{Z}^d$…

We consider one-dimensional excited random walks with finitely many cookies at each site. There are certain natural monotonicity results that are known for the excited random walk under some partial orderings of the cookie environments. We…

We prove a law of large numbers for random walks in certain kinds of i.i.d. random environments in Z^d that is an extension of a result of Bolthausen, Sznitman and Zeitouni (2003). We use this result, along with the lace expansion for…

In this paper, we study the random walk on a supercritical branching process with an uncountable and unbounded set of types supported on the $d$-regular tree $\mathbb{T}_d$ ($d\geq 3$), namely the cluster $\mathcal{C}_\circ^h$ of the root…

We study a model of multi-excited random walk on a regular tree which generalizes the models of the once excited random walk and the digging random walk introduced by Volkov (2003). We show the existence of a phase transition of the…

The model of a tired random walker, whose jump-length decays exponentially in time, is proposed and the motion of such a tired random walker is studied systematically in one, two and three dimensional contin- uum. In all cases, the…