Equilibrium fluctuations for exclusion processes with conductances in random environments. (English) Zbl 1196.60161
Summary: Fix a function \(W: \mathbb R^d \to \mathbb R\) such that \(W(x_1, \dots, x_d) = \sum^d_{k=1} W_k (x_k)\), where \(d \geq 1\), and each function \(W_k : \mathbb R \to \mathbb R\) is strictly increasing, right continuous with left limits. We prove the equilibrium fluctuations for exclusion processes with conductances, induced by \(W\), in random environments, when the system starts from an equilibrium measure. The asymptotic behavior of the empirical distribution is governed by the unique solution of a stochastic differential equation taking values in a certain nuclear Fréchet space.
MSC:
| 60K35 | Interacting random processes; statistical mechanics type models; percolation theory |
| 35B27 | Homogenization in context of PDEs; PDEs in media with periodic structure |
| 60F05 | Central limit and other weak theorems |
| 46A11 | Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.) |
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