Loop-erased walks and total positivity
Combinatorics
2007-05-23 v1 Probability
Rings and Algebras
Abstract
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.
Cite
@article{arxiv.math/0004083,
title = {Loop-erased walks and total positivity},
author = {Sergey Fomin},
journal= {arXiv preprint arXiv:math/0004083},
year = {2007}
}
Comments
20 pages; 7 figures