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Abstract: The link between a particular class of growth processes and random matriceswas established in the now famous 1999 article of Baik, Deift, and Johansson onthe length of the longest increasing subsequence of a random permutation.During the past ten years, this connection has been worked out in detail andled to an improved understanding of the large scale properties ofone-dimensional growth models. The reader will find a commented list ofreferences at the end. Our objective is to provide an introduction highlightingrandom matrices. From the outset it should be emphasized that this connectionis fragile. Only certain aspects, and only for specific models, the growthprocess can be reexpressed in terms of partition functions also appearing inrandom matrix theory.

Author: Patrik L. Ferrari 1, Herbert Spohn 2 1Bonn University, 2TU Munich

Source: https://arxiv.org/

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