Summary
In a famous paper [8] Hammersley investigated the lengthL n of the longest increasing subsequence of a randomn-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 [14, 11] relied on hard analysis of combinatorial asymptotics.
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Research supported by NSF Grant MCS 92-24857 and the Miller Institute for Basic Research in Science
Research supported by NSF Grant DMS92-04864
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Aldous, D., Diaconis, P. Hammersley's interacting particle process and longest increasing subsequences. Probab. Th. Rel. Fields 103, 199–213 (1995). https://doi.org/10.1007/BF01204214
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DOI: https://doi.org/10.1007/BF01204214
Mathematics Subject Classification (1979)
- 60C05
- 60K35