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November 1997 Increasing sequences of independent points on the planar lattice
Timo Seppäläinen
Ann. Appl. Probab. 7(4): 886-898 (November 1997). DOI: 10.1214/aoap/1043862416

Abstract

In 1977 Vershik and Kerov deduced the asymptotic normalized length of the longest increasing sequence among independent points uniformly distributed on the unit square. We solve the analogous problem for points on the planar square lattice that are present independently of each other.

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Timo Seppäläinen. "Increasing sequences of independent points on the planar lattice." Ann. Appl. Probab. 7 (4) 886 - 898, November 1997. https://doi.org/10.1214/aoap/1043862416

Information

Published: November 1997
First available in Project Euclid: 29 January 2003

zbMATH: 0897.60095
MathSciNet: MR1484789
Digital Object Identifier: 10.1214/aoap/1043862416

Subjects:
Primary: 60K35
Secondary: 60C05

Keywords: asymptotic shape , increasing sequences , Ulam's problem

Rights: Copyright © 1997 Institute of Mathematical Statistics

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Vol.7 • No. 4 • November 1997
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