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Gaussian bounds for discrete (graph) Dirichlet heat kernel

You can get a reasonable estimate by splitting time in three pieces, say [0,t/3], [t/3,2t/3], [2t/3,t] and estimating from above by the product of --- the probability starting at x of staying in the d …
Greg Lawler's user avatar
3 votes

Non-erasure probability in a loop-erased random walk in three dimensions

You are restating the fundamental hard problem in this area. You are writing down the probability that the nth point on the simple random walk is not erased. Summing this from 0 to n gives the expec …
Greg Lawler's user avatar