Suppose you have the simple random walk on $L=\mathbb{Z}^n,$ and $A \subset L$ is a subset (in my case, the subset is a union of hyperplanes, so in particular infinite). There is a random variable $T(A)$ -- the expected time to get from the origin to $A.$ The question is: is there some standard technology to upper bound the expectation of $T?$ T(A)?$ Any particularly recommended things to read?
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hitting time of a subsetSuppose you have the simple random walk on $L=\mathbb{Z}^n,$ and $A \subset L$ is a subset (in my case, the subset is a union of hyperplanes, so in particular infinite). There is a random variable $T(A)$ -- the expected time to get from the origin to $A.$ The question is: is there some standard technology to upper bound the expectation of $T?$ Any particularly recommended things to read?
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