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• W2084946144 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 point sources along two boundaries of the square, and appropriately scaling the parameters gives a model in the Kardar–Parisi–Zhang universality class. Following works of Baik and Rains, and Prähofer and Spohn, we review the calculation of the scaled cumulative distribution, in which a particular Painlevé II transcendent plays a prominent role." @default.
• W2084946144 created "2016-06-24" @default.
• W2084946144 creator A5019351501 @default.
• W2084946144 date "2003-08-22" @default.
• W2084946144 modified "2023-10-18" @default.
• W2084946144 title "Growth models, random matrices and Painlev transcendents" @default.
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• W2084946144 doi "https://doi.org/10.1088/0951-7715/16/6/201" @default.
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