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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.

10 votes
4 answers
903 views

The distribution of the shortest path through $n$ points

In the big picture, I'd like to know: if I sample $n$ points uniformly at random in the unit square, what is the probability that the shortest path that visits each one of them is very small? More p …
Will Schaefer's user avatar
2 votes
1 answer
308 views

Probability of a contiguous sub-sequence with different elements

Let $a$ and $b$ be two positive integers, and say $b\gg a$. Let $S$ be a random sequence with $ab$ elements, whose entries are all integers from $1$ to $a$, such that each number from $1$ to $a$ appe …
Will Schaefer's user avatar