Loop-erased walks and total positivity

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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.
20 pages; 7 figures

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Combinatorics, Probability, Rings and Algebras, 15A48 (Primary) 05C50, 31C20, 60J65 (Secondary}

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http://salesiana.dossiersoluciones.com/handle/123456789/59018

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0004083
 http://arxiv.org/abs/math/0004083

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arXiv