Hammersley's Interacting Particle Process and Longest Increasing Subsequences
نویسنده
چکیده
In a famous paper 8] Hammersley investigated the length L n of the longest increasing subsequence of a random n-permutation. Implicit in that paper is a certain one-dimensional continuous-space interacting particle process. By studying a hydrodynamical limit for Hammersley's process we show by fairly \soft" arguments that limn ?1=2 EL n = 2. This is a known result, but previous proofs (Vershik-Kerov 14]; Logan-Shepp 11]) relied on hard analysis of combinatorial asymptotics.
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