Related papers: New high-dimensional examples of ballistic random …
For more than a century lattice random walks have been employed ubiquitously, both as a theoretical laboratory to develop intuition about more complex stochastic processes and as a tool to interpret a vast array of empirical observations.…
We study the limit behaviour of a class of random walk models taking values in the $d$-dimensional unit standard simplex, $d\ge 1$, defined as follows. From an interior point $z$, the process chooses one of the $d+1$ vertices of the…
Let $(Z_n)_{n\in\N}$ be a $d$-dimensional {\it random walk in random scenery}, i.e., $Z_n=\sum_{k=0}^{n-1}Y(S_k)$ with $(S_k)_{k\in\N_0}$ a random walk in $\Z^d$ and $(Y(z))_{z\in\Z^d}$ an i.i.d. scenery, independent of the walk. The…
Random walks in random scenery are processes defined by $Z_n:=\sum_{k=1}^n\xi_{X_1+...+X_k}$, where $(X_k,k\ge 1)$ and $(\xi_y,y\in{\mathbb Z}^d)$ are two independent sequences of i.i.d. random variables with values in ${\mathbb Z}^d$ and…
We consider the branching capacity of the range of a simple random walk on $\mathbb Z^d$, with $d \ge 5$, and show that it falls in the same universality class as the volume and the capacity of the range of simple random walks and branching…
We derive a local limit theorem for normal, moderate, and large deviations for symmetric simple random walk on the square lattice in dimensions one and two that is an improvement of existing results for points that are particularly distant…
We define a random walk of a particle in $\mathbb{R}^3$ where the space is rotating. The particle is not glued to the space and will collide with it at random times, resulting in changes in its velocity and direction. After many collisions,…
This paper enhances the result of the work [G. Kozma, B. T\'oth, Ann. Probab. vol. 45 (2017) 4307-4347] . We prove the central limit theorem (in probability w.r.t. the environment) for the displacement of a random walker in divergence-free…
A recently developed model of random walks on a $D$-dimensional hyperspherical lattice, where $D$ is {\sl not} restricted to integer values, is extended to include the possibility of creating and annihilating random walkers. Steady-state…
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 study an extension of the generalized excited random walk (GERW) on $\mathbb{Z}^d$ introduced in [Ann. Probab. 40 (5), 2012, [7]] by Menshikov, Popov, Ram\'irez and Vachkovskaia. Our extension consists in studying a version of the GERW…
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…
The quenched and annealed large deviations of the random walk in random environment are shown to conform on any compact set whenever the level of disorder is sufficiently low. In this work, we show that these two large deviations always…
We present several refinements on the fluctuations of sequences of random vectors (with values in the Euclidean space $\mathbb{R}^d$) which converge after normalization to a multidimensional Gaussian distribution. More precisely we refine…
We consider a one dimensional sub-ballistic random walk evolving in a parametric i.i.d. random environment. We study the asymptotic properties of the maximum likelihood estimator (MLE) of the parameter based on a single observation of the…
We consider a random walk with transition probabilities weakly dependent on an environment with a deterministic, but strongly chaotic, evolution. We prove that for almost all initial conditions of the environment the walk satisfies the CLT.
Consider a supercritical branching random walk on the real line. The consistent maximal displacement is the smallest of the distances between the trajectories followed by individuals at the $n$th generation and the boundary of the process.…
It is conjectured that in dimensions $d\ge 2$ any random walk in an i.i.d. uniformly elliptic random environment (RWRE) which is directionally transient is ballistic. The ballisticity conditions for RWRE somehow interpolate between…
In this note, we consider random walks in the quarter plane with arbitrary big jumps. We announce the extension to that class of models of the analytic approach of [G. Fayolle, R. Iasnogorodski, and V. Malyshev, Random walks in the quarter…
We consider a model for random walks on random environments (RWRE) with random subset of the d-dimensional Euclidean lattice as the vertices, and uniform transition probabilities on 2d points (two "coordinate nearest points" in each of the…