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Answer by Lucia for Lattice random walk under gravity

Let $E_n$ denote the probability of the first return after $n$ steps, and let $P_n$ denote the probability of return after $n$ steps (but not necessarily the first return). Note that $E_n=P_n=0$ if $n$...

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Lattice random walk under gravity

Suppose a random walk on $\mathbb{Z}^2$ takes a step left or right withprobability $\frac{1}{4}$, but up with probability $\frac{1}{2} p$and down with probability $\frac{1}{2} (1-p)$, where $p \in...

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