Celebratio Mathematica — Liggett — Complete Bibliography

Complete Bibliography

Works connected to Thomas Richthammer

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P. Caputo, T. M. Liggett, and T. Richthammer: “Proof of Aldous’ spectral gap conjecture,” J. Am. Math. Soc. 23 : 3 (2010), pp. 831–851. MR 2629990 Zbl 1203.60145 ArXiv 0906.1238 article

Aldous’ spectral gap conjecture asserts that on any graph the random walk process and the random transposition (or interchange) process have the same spectral gap. We prove the conjecture using a recursive strategy. The approach is a natural extension of the method already used to prove the validity of the conjecture on trees. The novelty is an idea based on electric network reduction, which reduces the problem to the proof of an explicit inequality for a random transposition operator involving both positive and negative rates. The proof of the latter inequality uses suitable coset decompositions of the associated matrices with rows and columns indexed by permutations.

Pietro Caputo	Related
Thomas Richthammer	Related

G. R. Grimmett, T. M. Liggett, and T. Richthammer: “Percolation of arbitrary words in one dimension,” Random Structures Algorithms 37 : 1 (2010), pp. 85–99. MR 2674622 Zbl 1202.60155 ArXiv 0807.1676 article

Geoffrey Richard Grimmet	Related
Thomas Richthammer	Related