论文信息 - Range of cube-indexed random walk

Range of cube-indexed random walk

For given finite, connected, bipartite graphG=(V,E) with distinguishedν0 ∈V, set {fx189-1} Our main result says there is a fixedb so that whenG is a Hamming cube ({0, 1}n with the usual adjacency), andf is chosen uniformly fromF, the probability thatf takes more thanb values is at most e−Ω(n). this settles in a very strong way a conjecture of I. Benjamini, O. Häggström and E. Mossel [2].The proof is based on entropy considerations and a new log-concavity result.

Jeff Kahn | J. Kahn

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