Related papers: Hydrodynamics for the partial exclusion process in…
In \cite{J} M. Jara has presented a method, reducing the proof of the hydrodynamic limit of symmetric exclusion processes to an homogenization problem, as unified approach to recent works on the field as \cite{N}, \cite{F1}, \cite{F2} and…
We obtain the hydrodynamic limit of one-dimensional interacting particle systems describing the macroscopic evolution of the density of mass in infinite volume from the microscopic dynamics. The processes are weak pertubations of the…
Let $\Lambda$ be a connected closed region with smooth boundary contained in the $d$-dimensional continuous torus $\bb T^d$. In the discrete torus $N^{-1} \bb T^d_N$, we consider a nearest neighbor symmetric exclusion process where…
We consider random walks in random environments on Z^d. Under a transitivity hypothesis that is much weaker than the customary ellipticity condition, and assuming an absolutely continuous invariant measure on the space of the environments,…
We extend the usual hydrodynamic description of the symmetric exclusion process by keeping track of collision events corresponding to jumps into already occupied sites, thereby quantifying the dissipated part of the microscopic activity…
We construct a non reversible exclusion process with Bernoulli product invariant measure and having, in the diffusive hydrodynamic scaling, a non symmetric diffusion matrix, that can be explicitly computed. The antisymmetric part does not…
We introduce and study analytically and numerically a simple model of inter-agent competition, where underachievement is strongly discouraged. We consider $N\gg 1$ particles performing independent Brownian motions on the line. Two particles…
We consider a class of generalized long-range exclusion processes evolving either on $\mathbb Z$ or on a finite lattice with an open boundary. The jump rates are given in terms of a general kernel depending on both the departure and…
The collective non-equilibrium dynamics of multi-component mixtures of interacting active (self-propelled) and passive (diffusive) particles have garnered great interest in the physics community. However, the mathematical understanding of…
It is known that the competitive exclusion principle holds for a large kind of models involving several species competing for a single resource in an homogeneous environment. Various works indicate that the coexistence is possible in an…
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 consider a system consisting of a planar random walk on a square lattice, submitted to stochastic elementary local deformations. Depending on the deformation transition rates, and specifically on a parameter $\eta$ which breaks the…
We consider the hydrodynamic behavior of some conservative particle systems with degenerate jump rates without exclusive constraints. More precisely, we study the particle systems without restrictions on the total number of particles per…
In this paper, we are concerned with a class of conservative systems including asymmetric exclusion processes and zero-range processes as examples, where some particles are initially placed on $N$ positions. A particle jumps from a position…
We study the hydrodynamic and hydrostatic limits of the one-dimensional open symmetric inclusion process with slow boundary. Depending on the value of the parameter tuning the interaction rate of the bulk of the system with the boundary, we…
We study condensation in several particle systems related to the inclusion process. For an asymmetric one-dimensional version with closed boundary conditions and drift to the right, we show that all but a finite number of particles condense…
In this paper, we give the moderate deviation principle from the hydrodynamic limit of the simple exclusion process on $1$-dimensional torus starting from a nonequilibrium state, which extends the result given in Gao and Quastel (2003)…
We give a new approach to the well-known convergence to the hydrodynamic limit for the symmetric simple exclusion process (SSEP). More precisely, we characterize any possible limit of its empirical density measures as solutions to the heat…
By generalizing a class of models recently introduced to account for protracted transients in biological systems, we identify a novel mechanism for hyperuniformity. In this model, competition of particles over a shared resource guides the…
We demonstrate exciting similarities between classical and quantum many body systems whose microscopic dynamics are composed of non-reciprocal three-site facilitated exclusion processes. We show that the quantum analogue of the classical…