One-dimensional stochastic growth and Gaussian ensembles of random matrices

Details One-dimensional stochastic growth and Gaussian ensembles of random matrices One-dimensional stochastic growth and Gaussian ensembles of random matrices

2005-05-13

arxiv.org/abs/math-ph/0505038v2

In proceedings of ''Inhomogeneous Random Systems 2005'', Markov Processes Relat. Fields 12 (2006) 203-234

Physics

Mathematical Physics

34 pages, 8 figures; Review for the Inhomogeneous Random Systems 2005 proceedings; Final version

Scientific paper

In this review paper we consider the polynuclear growth (PNG) model in one spatial dimension and its relation to random matrix ensembles. For curved and flat growth the scaling functions of the surface fluctuations coincide with limit distribution functions coming from certain Gaussian ensembles of random matrices. This connection can be explained via point processes associated to the PNG model and the random matrices ensemble by an extension to the multilayer PNG and multi-matrix models, respectively. We also explain other models which are equivalent to the PNG model: directed polymers, the longest increasing subsequence problem, Young tableaux, a directed percolation model, kink-antikink gas, and Hammersley process.

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