Ulam’s Problem And Hammersley’s Process
Open Access
- 1 April 2001
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Probability
- Vol. 29 (2) , 683-690
- https://doi.org/10.1214/aop/1008956689
Abstract
Let Ln be the length of the longest increasing subsequence of a random permutation of the numbers 1, . . . , 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 limn!1 ELn/ p n = 2. We show in this note that the latter result is in fact an immediate consequence of properties of a random 2-dimensional signedKeywords
This publication has 7 references indexed in Scilit:
- Longest increasing subsequences: from patience sorting to the Baik-Deift-Johansson theoremBulletin of the American Mathematical Society, 1999
- On the distribution of the length of the longest increasing subsequence of random permutationsJournal of the American Mathematical Society, 1999
- A Microscopic Model for the Burgers Equation and Longest Increasing SubsequencesElectronic Journal of Probability, 1996
- Hammersley's interacting particle process and longest increasing subsequencesProbability Theory and Related Fields, 1995
- A variational problem for random Young tableauxAdvances in Mathematics, 1977
- Subadditive Ergodic TheoryThe Annals of Probability, 1973
- A FEW SEEDLINGS OF RESEARCHPublished by University of California Press ,1972