Hammersley's interacting particle process and longest increasing subsequences

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 lim n ′1/2 EL n =2. This is a known result, but previous proofs [14, 11] relied on hard analysis of combinatorial asymptotics. © 1995 Springer-Verlag