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

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

2007-05-27

arxiv.org/abs/0705.3925v1

Physics

Mathematical Physics

21 pages, 5 figures

Scientific paper

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.

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