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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.
3
votes
Non-erasure probability in a loop-erased random walk in three dimensions
You are restating the fundamental hard problem in this area. You are writing down the probability that the nth point on the simple random walk is not erased. Summing this from 0 to n gives the expec …