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April 2001 Ulam’s Problem And Hammersley’s Process
Piet Groeneboom
Ann. Probab. 29(2): 683-690 (April 2001). DOI: 10.1214/aop/1008956689

Abstract

Let $L_n$ be the length of the longest increasing subsequence of a random permutation of the numbers $1,\ldots, n$, for the uniform distribution on the set of permutations. Hammersley's interacting particle process, implicit in Hammersley (1972), has been used in Aldous and Diaconis (1995) to provide a “soft” hydrodynamical argument for proving that $\lim_{n \to \infty} EL_n / \sqrt{n} = 2$. We show in this note that the latter result is in fact an immediate consequence of properties of a random 2­dimensional signed measure, associated with Hammersley’s process.

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Piet Groeneboom. "Ulam’s Problem And Hammersley’s Process." Ann. Probab. 29 (2) 683 - 690, April 2001. https://doi.org/10.1214/aop/1008956689

Information

Published: April 2001
First available in Project Euclid: 21 December 2001

zbMATH: 1013.60003
MathSciNet: MR1849174
Digital Object Identifier: 10.1214/aop/1008956689

Subjects:
Primary: 60C05 , 60K35
Secondary: 60F05

Keywords: Hammersley's process , Longest increasing subsequence, , , Ulam's problem

Rights: Copyright © 2001 Institute of Mathematical Statistics

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Vol.29 • No. 2 • April 2001
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