Related papers: Explosivity in 1-d Activated Random Walk

Models of random walks are considered in which walkers are born at one location and die at all other locations with uniform death rate. Steady-state distributions of random walkers exhibit dimensionally dependent critical behavior as a…

For a subcritical Galton-Watson process $(\zeta_n)$, it is well known that under an $X \log X$ condition, the quotient $P(\zeta_n > 0)/ E\zeta_n$ has a finite positive limit. There is an analogous result for a (one-dimensional)…

We discuss activated escape from a metastable state of a system driven by a time-periodic force. We show that the escape probabilities can be changed very strongly even by a comparatively weak force. In a broad parameter range, the…

We show that it is possible to generate a random walk with an electrostatic field by means of several parallel infinite charged planes in which the surface charge distribution could be either $\pm\sigma$. We formulate the problem of this…

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…

It is shown that adiabatic cycles excite a quantum particle, which is confined in a one-dimensional region and is initially in an eigenstate. During the cycle, an infinitely sharp wall is applied and varied its strength and position. After…

Given a DFA we consider the random walk that starts at the initial state and at each time step moves to a new state by taking a random transition from the current state. This paper shows that for typical DFA this random walk induces an…

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,…

Let $(G,\mu)$ be a uniformly elliptic random conductance graph on $\mathbb{Z}^d$ with a Poisson point process of particles at time $t=0$ that perform independent simple random walks. We show that inside a cube $Q_K$ of side length $K$, if…

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 show that for each $\lambda \in [\frac{1}{2}, 1]$, there exists a solvable group and a finitely supported measure such that the associated random walk has upper speed exponent $\lambda$.

We consider Activated Random Walk (ARW), a model which generalizes the Stochastic Sandpile, one of the canonical examples of self organized criticality. Informally ARW is a particle system on $\mathbb{Z}$ with mass conservation. One starts…

We present a "black box" proof of mean-field near-critical behaviour for a family of functions on $\mathbb Z^d$ (${d>2}$) satisfying a short list of assumptions. The functions represent two-point functions of a lattice statistical…

We consider a random walk among a Poisson system of moving traps on ${\mathbb Z}$. In earlier work [DGRS12], the quenched and annealed survival probabilities of this random walk have been investigated. Here we study the path of the random…

Consider a one dimensional simple random walk $X=(X_n)_{n\geq0}$. We form a new simple symmetric random walk $Y=(Y_n)_{n\geq0}$ by taking sums of products of the increments of $X$ and study the two-dimensional walk…

We consider a specific random graph which serves as a disordered medium for a particle performing biased random walk. Take a two-sided infinite horizontal ladder and pick a random spanning tree with a certain edge weight $c$ for the…

Using renewal times and Girsanov's transform, we prove that the speed of the excited random walk is infinitely differentiable with respect to the bias parameter in $(0,1)$ for the dimension $d\ge 2$. At the critical point $0$, using a…

In this work, we study the effect of a moving detector on a discrete time one dimensional Quantum Random Walk where the movement is realized in the form of hopping/shifts. The occupation probability $f(x,t;n,s)$ is estimated as the number…

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…

In this paper, we consider the subcritical branching random walk in a random environment. We assume the branching and the step jump are independent; and the branching is in random envirenment, i.e., the particles in generation $n$ produce…