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Hammersley's interacting particle process and longest increasing subsequences
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  • Published: June 1995

Hammersley's interacting particle process and longest increasing subsequences

  • D. Aldous1 &
  • P. Diaconis2 

Probability Theory and Related Fields volume 103, pages 199–213 (1995)Cite this article

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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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References

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Author information

Authors and Affiliations

  1. Department of Statistics, University of California, 94720, Berkeley, CA, USA

    D. Aldous

  2. Department of Mathematics, Harvard University, 02138, Cambridge, MA, USA

    P. Diaconis

Authors
  1. D. Aldous
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  2. P. Diaconis
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Additional information

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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  • Received: 10 May 1994

  • Revised: 14 March 1995

  • Issue Date: June 1995

  • DOI: https://doi.org/10.1007/BF01204214

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Mathematics Subject Classification (1979)

  • 60C05
  • 60K35
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