Bulk Diffusion of 1D Exclusion Process with Bond Disorder

A. Faggionato

2007, v.13, Issue 3, 519-542

ABSTRACT

Given a doubly infinite sequence of positive numbers $\{c_k : k\in Z \}$ such that $\{c_k^{-1} : k\in Z\}$ satisfies a LLN with limit $\alpha\in (0,\infty]$, we consider the nearest-neighbor simple exclusion process on $Z$ where $c_k$ is the probability rate of jumps between $k$ and $k+1$. If $\alpha=\infty$ we require an additional minor technical condition. By extending a method developed in [K. Nagy, Symmetric random walk in random environment. Period. Math. Hung., 2002, v. 45, pp.101-120] we show that the diffusively rescaled process has hydrodynamic behavior described by the heat equation with diffusion constant $1/\alpha$. In particular, the process has diffusive behavior for $\alpha < \infty$ and subdiffusive behavior for $\alpha=\infty$.

Keywords: interacting particle systems,hydrodynamic limits,disorderedsystems,random walks in random environment