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42 votes
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Random walk inside a random walk inside...

Question 0: $G'$ is known as the trace of the random walk. Question 1: $G'$ is always recurrent with probability one. This is a result of Benjamini, Gurel-Gurevich, and Lyons from 2007. Question 2: …
Louigi Addario-Berry's user avatar
14 votes
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Random permutations of Z_n

I emailed Noga to ask him; here is his response (touched up slightly for MO; any errors in what I post are probably mine rather than Noga's). The only details not present are the required applications …
Louigi Addario-Berry's user avatar
34 votes
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When do 3D random walks return to their origin?

For a fairly robust intuitive argument, think of a random walk in $\mathbb{R}^d$ as the "product" of $d$ one-dimensional walks in $\mathbb{R}^1$. For a (finite variance) random walk in $\mathbb{R}^1$, …
Louigi Addario-Berry's user avatar