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Percolation and Random Walks

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Consider the two dimensional lattice and keep every edge with probability p, independently over different edges. It is known that there exists a critical probability p_c so that for all p > p_c there exists a unique infinite connected component. But how well connected is this infinite cluster? One way to evaluate this is by examining the rate of spread of a simple random walk on the cluster.

This talk is part of the Trinity Mathematical Society series.

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