Related papers: Universality Conjectures for Activated Random Walk
A random walk is known as a random process which describes a path including a succession of random steps in the mathematical space. It has increasingly been popular in various disciplines such as mathematics and computer science.…
Quantum walks and random walks bear similarities and divergences. One of the most remarkable disparities affects the probability of finding the particle at a given location: typically, almost a flat function in the first case and a…
The unreduced, universally nonperturbative analysis of arbitrary many-body interaction process reveals the irreducible, purely dynamic source of randomness. It leads to the universal definition of real system complexity (physics/9806002),…
We consider systems whose steady-states exhibit a nonequilibrium phase transition from an active state to one -among an infinite number- absorbing state, as some control parameter is varied across a threshold value. The pair contact…
We consider bond percolation on the square lattice with perfectly correlated random probabilities. According to scaling considerations, mapping to a random walk problem and the results of Monte Carlo simulations the critical behavior of the…
We discuss conditions for unique ergodicity of a collective random walk on a continuous circle. Individual particles in this collective motion perform independent (and different in general) random walks conditioned by the assumption that…
Quantum physics enables parameter estimation with precisions beyond the capability of classical sensors. Quantum criticality is a key resource for this quantum-enhanced sensing, but experimental realization has been challenging due to the…
We consider annihilating random walks on the finite one-dimensional integer torus with deposition of pairs of particles, conditioned on an atypical jump activity. All cumulants of the activity, defined as the number of particle jumps up to…
We consider a system of independent one-dimensional random walks in a common random environment under the condition that the random walks are transient with positive speed $v_P$. We give upper bounds on the quenched probability that at…
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 consider activated random walk (ARW), an interacting particle system and prototypical model of self-organized criticality in a setting which combines mean-field behavior with the geometry of an arbitrary graph, which we call the village…
We study a particle system with hopping (random walk) dynamics on the integer lattice $\mathbb Z^d$. The particles can exist in two states, active or inactive (sleeping); only the former can hop. The dynamics conserves the number of…
In this paper we study a random walk in a one-dimensional dynamic random environment consisting of a collection of independent particles performing simple symmetric random walks in a Poisson equilibrium with density $\rho \in (0,\infty)$.…
Quantum walks are powerful tools not only to construct the quantum speedup algorithms but also to describe specific models in physical processes. Furthermore, the discrete time quantum walk has been experimentally realized in various…
Consideration is given to the continuous-time supercritical branching random walk over a multidimensional lattice with a finite number of particle generation sources of the same intensity both with and without constraint on the variance of…
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…
Although quantum walks exhibit peculiar properties that distinguish them from random walks, classical behavior can be recovered in the asymptotic limit by destroying the coherence of the pure state associated to the quantum system. Here I…
Random walk is a fundamental concept with applications ranging from quantum physics to econometrics. Remarkably, one specific model of random walks appears to be ubiquitous across many fields as a tool to analyze transport phenomena in…
Self-organized criticality has been proposed to be a universal mechanism for the emergence of scale-free dynamics in many complex systems, and possibly in the brain. While such scale-free patterns were identified experimentally in many…
Random walk in random environment (RWRE) is a fundamental model of statistical mechanics, describing the movement of a particle in a highly disordered and inhomogeneous medium as a random walk with random jump probabilities. It has been…