Symmetric simple exclusion process in dynamic environment: hydrodynamics

Symmetric Simple Exclusion Process: Regularity of the Self Diffusion Coefficient

Part 3: Rigorous Proof of Hydrodynamics for Symmetric Simple Exclusion Processes

Step 1. Consider the trajectory of empirical measures indexed in an interval of time, π = 〈π N2t : t ∈ [0, T ]〉. Here, T > 0 is time length, fixed throughout. Let Q be the law of the trajectory. The first step is to show that the laws {Q : N ≥ 1} are tight in the space of measure-valued right-continuous trajectories with left limits, D([0, T ];M+). Moreover, this tightness will be shown in the ...

Totally asymmetric simple exclusion process

Unlike equilibrium statistical mechanics non-equilibrium statistical mechanics (NESM) has no wellestablished framework. The totally asymmetric simple exclusion process (TASEP) is one of the few models available that try to meet the challenge of describing NESM. Here TASEP is presented in its simplest version. Further two biological applications on mRNA translation and molecular motors are prese...

Gaussian estimates for symmetric simple exclusion processes

2014 We prove Gaussian tail estimates for the transition probability of n particles evolving as symmetric exclusion processes on Zd, improving results obtained in [9]. We derive from this result a non-equilibrium Boltzmann-Gibbs principle for the symmetric simple exclusion process in dimension 1 starting from a product measure with slowly varying parameter. RÉSUMÉ. 2014 We prove Gaussian tail e...

Distributional Limits for the Symmetric Exclusion Process

Strong negative dependence properties have recently been proved for the symmetric exclusion process. In this paper, we apply these results to prove convergence to the Poisson and Gaussian distributions for various functionals of the process.