Large deviations for increasing sequences on the plane |
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Authors: | Timo Seppäläinen |
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Institution: | (1) Department of Mathematics, Iowa State University, Ames, IA 50011-2064, USA. e-mail: seppalai@iastate.edu, US |
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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.
Received: 22 July 1997 / Revised version: 23 March 1998 |
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Keywords: | Mathematics Subject Classification (1991): Primary 60F10 Secondary 60C05 60K35 |
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