Loop-erased walks and total positivity

Details Loop-erased walks and total positivity Loop-erased walks and total positivity

2000-04-12

arxiv.org/abs/math/0004083v1

Mathematics

Combinatorics

20 pages; 7 figures

Scientific paper

We consider matrices whose elements enumerate weights of walks in planar directed weighted graphs (not necessarily acyclic). These matrices are totally nonnegative; more precisely, all their minors are formal power series in edge weights with nonnegative coefficients. A combinatorial explanation of this phenomenon involves loop-erased walks. Applications include total positivity of hitting matrices of Brownian motion in planar domains.

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