Related papers: Generalized Hammersley Process and Phase Transitio…
We prove results for random walks in dynamic random environments which do not require the strong uniform mixing assumptions present in the literature. We focus on the "environment seen from the walker"-process and in particular its…
The diffusion of a particle in a crowded environment typically proceeds through three regimes: for very short times the particle diffuses freely until it collides with an obstacle for the first time, while for very long times diffusion the…
We prove that for the Activated Random Walks model on transitive unimodular graphs, if there is fixation, then every particle eventually fixates, almost surely. We deduce that the critical density is at most 1. Our methods apply for much…
Transition out of a topological phase is typically characterized by discontinuous changes in topological invariants along with bulk gap closings. However, as a clean system is geometrically punctured, it is natural to ask the fate of an…
We theoretically study the transport properties of self-propelled particles on complex structures, such as motor proteins on filament networks. A general master equation formalism is developed to investigate the persistent motion of…
Considering the dynamics of non-interacting particles randomly moving on a lattice, the occurrence of a discontinuous transition in the values of the lattice parameters (lattice spacing and hopping times) determines the uprisal of two…
Many biological processes are supported by special molecules, called motor proteins or molecular motors, that transport cellular cargoes along linear protein filaments and can reversibly associate to their tracks. Stimulated by these…
In this paper we study the kinetics of diffusion-limited, pseudo-first-order A + B -> B reactions in situations in which the particles' intrinsic reactivities vary randomly in time. That is, we suppose that the particles are bearing "gates"…
The emergence of heavy-tailed statistics in complex systems is conventionally attributed to non-local stochastic jumps or non-Markovian memory. Here, we present a one-dimensional random walk where power-law behaviors arise instead from a…
We consider a last passage percolation model in dimension $1+1$ with potential given by the product of a spatial i.i.d. potential with symmetric bounded distribution and an independent i.i.d. in time sequence of signs. We assume that the…
We study a model of bacterial dynamics where two interacting random walkers perform run-and-tumble motion on a one-dimensional lattice under mutual exclusion and find an exact expression for the probability distribution in the steady state.…
We study the stochastic dynamics of a particle with two distinct motility states. Each one is characterized by two parameters: one represents the average speed and the other represents the persistence quantifying the tendency to maintain…
The intensely studied measurement-induced entanglement phase transition has become a hallmark of non-unitary quantum many-body dynamics. Usually, such a transition only shows up at the level of each individual quantum trajectory, and is…
When particles move through a crystal or optical lattice, their motion can sometimes become frozen by strong external forces -- yet collective motion may still emerge through subtle many-body effects. In this work, we explore such…
Natural phenomena frequently involve a very large number of interacting molecules moving in confined regions of space. Cellular transport by motor proteins is an example of such collective behavior. We derive a deterministic compartmental…
We study an active random walker model in which a particle's motion is determined by a self-generated field. The field encodes information about the particle's path history. This leads to either self-attractive or self-repelling behavior.…
We study the behavior of random walk on dynamical percolation. In this model, the edges of a graph G are either open or closed and refresh their status at rate \mu\ while at the same time a random walker moves on G at rate 1 but only along…
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…
In recent years, several experiments highlighted a new type of diffusion anomaly, which was called Brownian yet non-Gaussian diffusion. In systems displaying this behavior, the mean squared displacement of the diffusing particles grows…
Experimental studies of the diffusion of biomolecules in the environment of biological cells are routinely confronted with multiple sources of stochasticity, whose identification renders the detailed data analysis of single molecule…