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Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
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An "inchworm-like" random walk on an integer interval
Imagine I place $k$ stones on an infinite one-dimensional integer interval $Z$ s.t. no stone is more than some distance $d$ from any other stone. For example, if $d=1$ and $k = 5$, we might place the …