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An invariance principle for reversible Markov processes. Applications to random motions in random environments. (English) Zbl 0713.60041
Summary: We present an invariance principle for antisymmetric functions of a reversible Markov process which immediately implies convergence to Brownian motion for a wide class of random motions in random environments. We apply it to establish convergence to Brownian motion (i) for a walker moving in the infinite cluster of the two-dimensional bond percolation model, (ii) for a d-dimensional walker moving in a symmetric random environment under very mild assumptions on the distribution of the environment, (iii) for a tagged particle in a d-dimensional symmetric lattice gas which allows interchanges, (iv) for a tagged particle in a d- dimensional system of interacting Brownian particles. Our formulation also leads naturally to bounds on the diffusion constant.

MSC:
60F17 Functional limit theorems; invariance principles
60K35 Interacting random processes; statistical mechanics type models; percolation theory
60J25 Continuous-time Markov processes on general state spaces
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