On Increasing Subsequences of I.I.D. Samples

Authors:
Jean-Dominique Deuschel;Ofer Zeitouni
Affiliations:
Technische Universität Berlin, Fachbereich Mathematik, TU-Berlin, Straße des 17. Juni 135, D-10623 Berlin, Germany (e-mail: deuschel@stoch1.math.tu-berlin.de);Department of Electrical Engineering, Technion, Haifa 32000, Israel (e-mail: zeitouni@ee.technion.ac.il)
Venue:
Combinatorics, Probability and Computing
Year:
1999

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Abstract

We study the fluctuations, in the large deviations regime, of the longest increasing sub-sequence of a random i.i.d. sample on the unit square. In particular, our results yield the precise upper and lower exponential tails for the length of the longest increasing subsequence of a random permutation.