Journal article

Growth models, random matrices and Painleve transcendents

PJ Forrester

NONLINEARITY | IOP PUBLISHING LTD | Published : 2003

Abstract

The Hammersley process relates to the statistical properties of the maximum length of all up/right paths connecting random points of a given density in the unit square from (0, 0) to (1, 1). This process can also be interpreted in terms of the height of the polynuclear growth model, or the length of the longest increasing subsequence in a random permutation. The cumulative distribution of the longest path length can be written in terms of an average over the unitary group. Versions of the Hammersley process in which the points are constrained to have certain symmetries of the square allow similar formulae. The derivation of these formulae is reviewed. Generalizing the original model to have ..

View full abstract

University of Melbourne Researchers