AbatractIn this talk, we consider random conductance models with stable-like long range jumps, and obtain the quenched invariance principle (QIP) and a quantitative version of stochastic homogenization for the scaled random walks with explicit polynomial rates up to logarithmic corrections.For QIP, we utilize probabilistic potential theory for the corresponding jump processes, and two essential...
Description: The central-limit type results are universal in many random walk models: they are known as Donsker’s theorem for the classical Zd random walk, and also hold for some random walks in random environment, even when the environment is degenerate like percolation. In their proofs, the homogenization theory, which comes from PDE, plays an important role. This course will cover the follo...
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