Related papers: Universality and Sharpness in Absorbing-State Phas…
At a continuous transition into a nonunique absorbing state, particle systems may exhibit nonuniversal critical behavior, in apparent violation of hyperscaling. We propose a generalized scaling theory for dynamic critical behavior at a…
We study the equilibrium phase diagram of a generalized ABC model on an interval of the one-dimensional lattice: each site $i=1,...,N$ is occupied by a particle of type $\a=A,B,C,$ with the average density of each particle species…
We investigate a modified version of the $AB$ random sequential adsorption model. Specifically, this model involves the deposition of two distinct types of particles onto a lattice, with the constraint that different types cannot occupy…
The coupling of branching-annihilating random walks to a static field with a local conservation law is shown to change the scaling properties of their phase transitions to absorbing states. In particular, we find that DP-class transitions…
We consider the statistics of occupation times, the number of visits at the origin and the survival probability for a wide class of stochastic processes, which can be classified as renewal processes. We show that the distribution of these…
We derive the first two moments of generic positive stochastic functionals in terms of the one- and two-time probability density functions of the underlying random walk, and we prove ergodicity of observables in stationary random walks.…
Mobility edge transitions from localized to extended states have been observed in two and three dimensional systems, for which sound theoretical explanations have also been derived. One-dimensional lattice models have failed to predict…
We study the stochastic motion of active particles that undergo spontaneous transitions between two distinct modes of motion. Each mode is characterized by a velocity distribution and an arbitrary (anti-)persistence. We present an…
Quantum walks are considered in a one-dimensional random medium characterized by static or dynamic disorder. Quantum interference for static disorder can lead to Anderson localization which completely hinders the quantum walk and it is…
We investigate the impact of decoherence and static disorder on the dynamics of quantum particles moving in a periodic lattice. Our experiment relies on the photonic implementation of a one-dimensional quantum walk. The pure quantum…
We study the asymptotic position distribution of general quantum walks on a lattice, including walks with a random coin, which is chosen from step to step by a general Markov chain. In the unitary (i.e., non-random) case, we allow any…
Motivated by various recent experimental findings, we propose a dynamical model of intermittently self-propelled particles: active particles that recurrently switch between two modes of motion, namely an active run-state and a turn state,…
Diffusion-coagulation can be simply described by a dynamic where particles perform a random walk on a lattice and coalesce with probability unity when meeting on the same site. Such processes display non-equilibrium properties with strong…
This paper concerns discrete-time occupancy processes on a finite graph. Our results can be formulated in two theorems, which are stated for vertex processes, but also applied to edge process (e.g., dynamic random graphs). The first theorem…
Let $r: S\times S\to \bb R_+$ be the jump rates of an irreducible random walk on a finite set $S$, reversible with respect to some probability measure $m$. For $\alpha >1$, let $g: \bb N\to \bb R_+$ be given by $g(0)=0$, $g(1)=1$, $g(k) =…
We study a symmetric random walk (RW) in one spatial dimension in environment, formed by several zones of finite width, where the probability of transition between two neighboring points and corresponding diffusion coefficient are…
In this paper, we study the dynamics of a random walker diffusing on a disordered one-dimensional lattice with random trappings. The distribution of escape probabilities is computed exactly for any strength of the disorder. These…
We consider a continuous-time symmetric branching random walk on multidimensional lattices with immigration and infinite number of initial particles. We assume that at every lattice point a process of birth and death of particles is…
The diffusive transport of particles in anisotropic media is a fundamental phenomenon in computational, medical and biological disciplines. While deterministic models (partial differential equations) of such processes are well established,…
Random walks are basic diffusion processes on networks and have applications in, for example, searching, navigation, ranking, and community detection. Recent recognition of the importance of temporal aspects on networks spurred studies of…