Random Growth Models

Details Random Growth Models Random Growth Models

2010-03-03

arxiv.org/abs/1003.0881v2

Mathematics

Probability

Review paper; 24 pages, 4 figures; Minor corrections

Scientific paper

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

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