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Large deviations for increasing sequences on the plane
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  • Published: October 1998

Large deviations for increasing sequences on the plane

  • Timo Seppäläinen1 

Probability Theory and Related Fields volume 112, pages 221–244 (1998)Cite this article

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Abstract.

We prove a large deviation principle with explicit rate functions for the length of the longest increasing sequence among Poisson points on the plane. The rate function for lower tail deviations is derived from a 1977 result of Logan and Shepp about Young diagrams of random permutations. For the upper tail we use a coupling with Hammersley's particle process and convex-analytic techniques. Along the way we obtain the rate function for the lower tail of a tagged particle in a totally asymmetric Hammersley's process.

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Authors and Affiliations

  1. Department of Mathematics, Iowa State University, Ames, IA 50011-2064, USA. e-mail: seppalai@iastate.edu, , , , , , US

    Timo Seppäläinen

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  1. Timo Seppäläinen
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Received: 22 July 1997 / Revised version: 23 March 1998

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Seppäläinen, T. Large deviations for increasing sequences on the plane. Probab Theory Relat Fields 112, 221–244 (1998). https://doi.org/10.1007/s004400050188

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  • Issue Date: October 1998

  • DOI: https://doi.org/10.1007/s004400050188

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  • Mathematics Subject Classification (1991): Primary 60F10; Secondary 60C05
  • 60K35
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