# Non equilibrium stationary state for the SEP with births and deaths

@inproceedings{Masi2012NonES, title={Non equilibrium stationary state for the SEP with births and deaths}, author={Anna de Masi and Errico Presutti and Dimitrios K. Tsagkarogiannis and Maria Eulalia Vares}, year={2012} }

This paper is a follow-up of the study initiated in [1], [2], where current reservoirs in the context of stochastic interacting particle systems have been proposed as a method to investigate stationary non-equilibrium states with steady currents produced by action at the boundary. Due to the particular difficulties in implementing this new method, we consider the simplest possible particle system. The bulk dynamics is the symmetric simple exclusion process (SSEP) in the interval ΛN = [−N,N…

## 8 Citations

Exclusion process with long jumps in contact with reservoirs

- Mathematics
- 2018

This thesis is devoted to the derivation of the hydrodynamic and the hydrostatic limit of the exclusion process with long jumps in the box ΛN = {1, . . . , N − 1}, for N ≥ 2, in contact with…

Fluctuation Limit for Interacting Diffusions with Partial Annihilations Through Membranes

- Mathematics
- 2014

We study fluctuations of the empirical processes of a non-equilibrium interacting particle system consisting of two species over a domain that is recently introduced in Chen and Fan (Ann Probab, to…

Exclusion Process with Slow Boundary

- Mathematics
- 2014

We study the hydrodynamic and the hydrostatic behavior of the simple symmetric exclusion process with slow boundary. The term slow boundary means that particles can be born or die at the boundary…

Non-equilibrium and stationary fluctuations of a slowed boundary symmetric exclusion

- PhysicsStochastic Processes and their Applications
- 2019

Slow to fast infinitely extended reservoirs for the symmetric exclusion process with long jumps

- Mathematics
- 2017

We consider an exclusion process with long jumps in the box $\Lambda_N=\{1, \ldots,N-1\}$, for $N \ge 2$, in contact with infinitely extended reservoirs on its left and on its right. The jump rate is…

Equilibrium fluctuations for the slow boundary exclusion process

- Mathematics
- 2015

We prove that the equilibrium fluctuations of the symmetric simple exclusion process in contact with slow boundaries is given by an Ornstein-Uhlenbeck process with Dirichlet, Robin or Neumann…

Large Deviations in the Symmetric Simple Exclusion Process with Slow Boundaries

- Physics, Mathematics
- 2020

We obtain the exact large deviation functions of the density profile and of the current, in the non-equilibrium steady state of a one dimensional symmetric simple exclusion process coupled to…

Hydrodynamics for SSEP with Non-reversible Slow Boundary Dynamics: Part I, the Critical Regime and Beyond

- Mathematics
- 2019

The purpose of this article is to provide a simple proof of the hydrodynamic and hydrostatic behavior of the SSEP in contact with slowed reservoirs which inject and remove particles in a finite size…

## References

SHOWING 1-3 OF 3 REFERENCES

Current Reservoirs in the Simple Exclusion Process

- Mathematics
- 2011

We consider the symmetric simple exclusion process in the interval [−N,N] with additional birth and death processes respectively on (N−K,N], K>0, and [−N,−N+K). The exclusion is speeded up by a…

Truncated correlations in the stirring process with births and deaths

- Mathematics
- 2011

We consider the stirring process in the interval $\Lambda_N:=[-N,N]$ of $\mathbb Z$ with births and deaths taking place in the intervals $I_+:=(N-K,N]$, and respectively $I_-:=[-N,-N+K)$, $1 \le K…

Interacting Particle Systems

- Mathematics
- 1985

The Construction, and Other General Results.- Some Basic Tools.- Spin Systems.- Stochastic Ising Models.- The Voter Model.- The Contact Process.- Nearest-Particle Systems.- The Exclusion Process.-…