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Invariance Principle and Local Limit Theorem for the Random Conductance Model

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If you have a question about this talk, please contact Lisa Maria Kreusser.

The random conductance model is a well-established model for a random walk in random environment. During the last decade the question whether a quenched invariance principle (or quenched functional central limit theorem) holds for the random walk and whether the associated heat kernel satisfies a quenched local limit theorem has been intensively studied. In situations where the environment is generated by unbounded conductances these questions turned out to be rather non-trivial because of the possibility that the random walk might get trapped. In this talk we will review recent results for the case of an ergodic, degenerate environment. We present a quenched invariance principle and a quenched local limit theorem for ergodic conductances satisfying a certain moment condition. This talk is based on joint work with Jean-Dominique Deuschel and Martin Slowik.

This talk is part of the Cambridge Analysts' Knowledge Exchange series.

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