Symmetrized models of last passage percolation and non-intersecting lattice paths

Abstract

It has been shown that the last passage time in certain symmetrized models of directed percolation can be written in terms of averages over random matrices from the classical groups $U(l)$, $Sp(2l)$ and $O(l)$. We present a theory of such results based on non-intersecting lattice paths, and integration techniques familiar from the theory of random matrices. Detailed derivations of probabilities relating to two further symmetrizations are also given.

21 pages, 5 figures

References in corpus (1)

• Exact solutions for KPZ-type growth processes, random matrices, and equilibrium shapes of crystals

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