相关论文: Existence of an infinite particle limit of stochas…

We consider the stochastic ranking process with space-time dependent jump rates for the particles. The process is a simplified model of the time evolution of the rankings such as sales ranks at online bookstores. We prove that the joint…

We consider the stochastic ranking process with the jump times of the particles determined by Poisson random measures. We prove that the joint empirical distribution of scaled position and intensity measure converges almost surely in the…

We consider the stochastic ranking process with space-time dependent unbounded jump rates for the particles. We prove that the joint empirical distribution of jump rate and scaled position converges almost surely to a deterministic…

Consider a system of infinitely many Brownian particles on the real line. At any moment, these particles can be ranked from the bottom upward. Each particle moves as a Brownian motion with drift and diffusion coefficients depending on its…

We study finite particle systems on the one-dimensional integer lattice, where each particle performs a continuous-time nearest-neighbour random walk, with jump rates intrinsic to each particle, subject to an exclusion interaction which…

We consider a finite number of particles characterised by their positions and velocities. At random times a randomly chosen particle, the follower, adopts the velocity of another particle, the leader. The follower chooses its leader…

We introduce and investigate a new model of a finite number of particles jumping forward on the real line. The jump lengths are independent of everything, but the jump rate of each particle depends on the relative position of the particle…

We consider an infinite system of particles in one dimension, each particle performs independant Sinai's random walk in random environment. Considering an instant $t$, large enough, we prove a result in probability showing that the…

We introduce and investigate a new model of a finite number of particles jumping forward on the real line. The jump lengths are independent of everything, but the jump rate of each particle depends on the relative position of the particle…

We study semi-infinite particle systems on the one-dimensional integer lattice, where each particle performs a continuous-time nearest-neighbour random walk, with jump rates intrinsic to each particle, subject to an exclusion interaction…

We consider a system of $N$ particles on the real line that evolves through iteration of the following steps: 1) every particle splits into two, 2) each particle jumps according to a prescribed displacement distribution supported on the…

We study an interacting particle system of a finite number of labelled particles on the integer lattice, in which particles have intrinsic masses and left/right jump rates. If a particle is the minimal-label particle at its site when it…

We study an interacting particle system whose dynamics depends on an interacting random environment. As the number of particles grows large, the transition rate of the particles slows down (perhaps because they share a common resource of…

We study a class of interacting particle systems on $\mathbb{R}$ with two types. Particles evolve by independent jumps sampled from a fixed distribution, with type-dependent jump rates $v_+$, $v_-$ and stochastic type switching driven by…

We consider the behaviour of branching-selection particle systems in the large population limit. The dynamics of these systems is the combination of the following three components: (a) Motion: particles move on the real line according to a…

We study a system consisting of $n$ particles, moving forward in jumps on the real line. Each particle can make both independent jumps, whose sizes have some distribution, or ``synchronization'' jumps, which allow it to join a randomly…

We consider a large family of branching-selection particle systems. The branching rate of each particle depends on its rank and is given by a function $b$ defined on the unit interval. There is also a killing measure $D$ supported on the…

We consider finite and infinite systems of particles on the real line and half-line evolving in continuous time. Hereby, the particles are driven by i.i.d. L\'{e}vy processes endowed with rank-dependent drift and diffusion coefficients. In…

Motivated by a general principle governing regulation mechanisms in biological cells, we investigate a general interaction scheme between different populations of particles and specific particles, referred to as agents. Assuming that each…

The position density of a "particle" performing a continuous-time quantum walk on the integer lattice, viewed on length scales inversely proportional to the time t, converges (as t tends to infinity) to a probability distribution that…