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We consider the asymmetric exclusion process. We start from a profile which is constant along the drift direction and prove that the density profile, under a diffusive rescaling of time, converges to the solution of a parabolic equation.

Probability · Mathematics 2009-11-10 C. Landim , R. M. Sued , G. Valle

We introduce a class of one dimensional deterministic models of energy-volume conserving interfaces. Numerical simulations show that these dynamics are genuinely super-diffusive. We then modify the dynamics by adding a conservative…

Statistical Mechanics · Physics 2015-05-28 Cédric Bernardin , Gabriel Stoltz

We consider a general class of nonlinear diffusive models with bulk dissipation and boundary driving, and derive its hydrodynamic description in the large size limit. Both the average macroscopic behavior and the fluctuating properties of…

Statistical Mechanics · Physics 2013-10-29 A. Prados , A. Lasanta , Pablo I. Hurtado

We derive the hydrodynamic limit of a kinetic equation where the interactions in velocity are modelled by a linear operator (Fokker-Planck or Linear Boltzmann) and the force in the Vlasov term is a stochastic process with high amplitude and…

Analysis of PDEs · Mathematics 2020-03-23 Arnaud Debussche , Julien Vovelle

We study a totally asymmetric simple exclusion process where jumps happen at rate one, except at the origin where the rate is lower. We prove a hydrodynamic scaling limit to a macroscopic profile described by a variational formula. The…

Probability · Mathematics 2007-05-23 Timo Seppalainen

Randomized load balancing networks arise in a variety of applications, and allow for efficient sharing of resources, while being relatively easy to implement. We consider a network of parallel queues in which incoming jobs with independent…

Probability · Mathematics 2017-10-13 Reza Aghajani , Kavita Ramanan

We consider a one-dimensional gradient symmetric exclusion process in mild contact with boundary reservoirs. The hydrodynamic limit of the empirical measure is given by a non-linear second-order parabolic equation with non-linear Robin…

Probability · Mathematics 2024-02-09 A. Bouley , C. Landim

We investigate the hydrodynamic behavior and local equilibrium of the multilane exclusion process, whose invariant measures were studied in our previous paper \cite{mlt1a}. The dynamics on each lane follows a hyperbolic time scaling,…

Probability · Mathematics 2025-02-03 Gideon Amir , Christophe Bahadoran , Ofer Busani , Ellen Saada

We consider hydrodynamic scaling limits for a class of reversible interacting particle systems, which includes the symmetric simple exclusion process and certain zero-range processes. We study a (non-quadratic) microscopic action functional…

Mathematical Physics · Physics 2018-12-19 Marcus Kaiser , Robert L. Jack , Johannes Zimmer

We consider hydrodynamic limits of interacting particles systems with open boundaries, where the exterior parameters change in a time scale slower than the typical relaxation time scale. The limit deterministic profiles evolve…

Probability · Mathematics 2016-01-20 Anna De Masi , Stefano Olla

We consider attractive particle systems in $\Z^d$ with product invariant measures. We prove that when particles are restricted to a subset of $\Z^d$, with birth and death dynamics at the boundaries, the hydrodynamic limit is given by the…

Probability · Mathematics 2011-09-05 Christophe Bahadoran

We study the hydrodynamic limit for three gradient spin models: generalized Kipnis-Marchioro-Presutti (KMP), its discrete version and a family of harmonic models, under symmetric and nearest-neighbor interactions. These three models share…

Probability · Mathematics 2025-05-19 Chiara Franceschini , Patrícia Gonçalves , Kohei Hayashi , Makiko Sasada

We consider the weakly asymmetric exclusion process on a bounded interval with particle reservoirs at the endpoints. The hydrodynamic limit for the empirical density, obtained in the diffusive scaling, is given by the viscous Burgers…

Probability · Mathematics 2009-12-14 Lorenzo Bertini , Claudio Landim , Mustapha Mourragui

In this article, we study the hydrodynamic limit for a stochastic interacting particle system whose dynamics consists in a superposition of several dynamics: the exclusion rule, that dictates that no more than a particle per site with a…

Probability · Mathematics 2024-09-06 Oslenne Araújo , Patrícia Gonçalves , Alexandre B. Simas

We consider a lattice model of active matter with exclusion and derive its hydrodynamic description exactly. The hydrodynamic limit leads to an integro-differential equation for the density of particles with a given orientation. Volume…

Mathematical Physics · Physics 2023-10-31 James Mason , Clement Erignoux , Robert Jack , Maria Bruna

We present a hydrodynamic theory describing pair diffusion in systems with periodic boundary conditions, thereby generalizing earlier work on self-diffusion [D\"unweg and Kremer, J. Chem. Phys. 1993, 99, 6983-6997; Yeh and Hummer, J. Phys.…

Soft Condensed Matter · Physics 2023-05-03 Diddo Diddens , Andreas Heuer

We describe the hydrodynamic behavior of the $k$-step exclusion process. Since the flux appearing in the hydrodynamic equation for this particle system is neither convex nor concave, the set of possible solutions include in addition to…

Probability · Mathematics 2010-11-10 Herve Guiol , Krishnamurthi Ravishankar , Ellen Saada

We consider the symmetric simple exclusion process in $\mathbb Z^d$ with quenched bounded dynamic random conductances and prove its hydrodynamic limit in path space. The main tool is the connection, due to the self-duality of the process,…

Probability · Mathematics 2021-02-03 Frank Redig , Ellen Saada , Federico Sau

We consider the out-of-equilibrium dynamics of an interacting integrable system in the presence of an external dephasing noise. In the limit of large spatial correlation of the noise, we develop an exact description of the dynamics of the…

Statistical Mechanics · Physics 2020-10-21 Alvise Bastianello , Jacopo De Nardis , Andrea De Luca

Considering the example of interacting Brownian particles we present a linear response derivation of the boundary condition for the corresponding hydrodynamic description (the diffusion equation). This requires us to identify a non-analytic…

Statistical Mechanics · Physics 2009-11-07 M. Fuchs , K. Kroy