相关论文: Random walk of second class particles in product s…

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,…

A convergence theorem is obtained for quantum random walks with particles in an arbitrary normal state. This result unifies and extends previous work on repeated-interactions models, including that of the author (2010, J. London Math. Soc.…

We investigate a branching random walk where the displacements are independent from the branching mechanism and have a stretched exponential distribution. We describe the positions of the particles in the vicinity of the rightmost particle…

Simple random walks are a basic staple of the foundation of probability theory and form the building block of many useful and complex stochastic processes. In this paper we study a natural generalization of the random walk to a process in…

Wavefunction collapse models modify Schr\"odinger's equation so that it describes the collapse of a superposition of macroscopically distinguishable states as a dynamical process. This provides a basis for the resolution of the quantum…

We consider a new model of a branching random walk on a multidimensional lattice with continuous time and one source of particle reproduction and death, as well as an infinite number of sources in which, in addition to the walk, only…

We have shown that the steady state probability distribution function of a diffusion-coalescence system on a one-dimensional lattice of length L with reflecting boundaries can be written in terms of a superposition of double shock…

We consider a continuous-time branching random walk on a multidimensional lattice with two types of particles and an infinite number of initial particles. The main results are devoted to the study of the generating function and the limiting…

We show that the product or convex combination of two Markov operators with equivalent stationary measures need not have a stationary measure from the same measure class. More specifically, we exhibit examples of a hitherto undescribed…

We discuss the approximate phenomenological description of the motion of a single second-class particle in a two-species totally asymmetric simple exclusion process (TASEP) on a 1D lattice. Initially, the second class particle is located at…

... but no other surprises in the zero range world. We check all nearest neighbour 1-dimensional asymmetric zero range processes for random walking product shock measures as demonstrated already for a few cases in the literature. We find…

In this paper we study some conditional probabilities for the totally asymmetric simple exclusion processes (TASEP) with second class particles. To be more specific, we consider a finite system with one first class particle and $N-1$ second…

Random walks on the circle group $\mathbb{R}/\mathbb{Z}$ whose elementary steps are lattice variables with span $\alpha \not\in \mathbb{Q}$ or $p/q \in \mathbb{Q}$ taken mod $\mathbb{Z}$ exhibit delicate behavior. In the rational case we…

We consider the one dimensional totally asymmetric simple exclusion process with initial product distribution with densities $0 \leq \rho_0 < \rho_1 <...< \rho_n \leq 1$ in $(-\infty,c_1\ve^{-1})$, $[c_1\ve^{-1},c_2\epsilon^{-1}),...,[c_n…

We consider random walks on the support of a random purely atomic measure on $\mathbb{R}^d$ with random jump probability rates. The jump range can be unbounded. The purely atomic measure is reversible for the random walk and stationary for…

We study a model of aggregation and fragmentation of clusters of particles on an open segment of a single-lane road. The particles and clusters obey the stochastic discrete-time discrete-space kinetics of the Totally Asymmetric Simple…

We consider simple exclusion processes on Z for which the underlying random walk has a finite first moment and a non-zero mean and whose initial distributions are product measures with different densities to the left and to the right of the…

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…

The $N$-particle branching random walk is a discrete time branching particle system with selection. We have $N$ particles located on the real line at all times. At every time step each particle is replaced by two offspring, and each…

Spontaneous collapse models use non-linear stochastic modifications of the Schroedinger equation to suppress superpositions of eigenstates of the measured observable and drive the state to an eigenstate. It was recently demonstrated that…