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Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.

6 votes
2 answers
2k views

Distribution of $\max_{n \ge 0} S_n$, random walk

Say we have a random walk that is a nearest neighbor random walk on the integers where at each step the probability of moving one step to the right is $p$ and the probability of moving one step to the …