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Media type:
E-Article
Title:
Loop-Erased Walks and Total Positivity
Contributor:
Fomin, Sergey
Published:
American Mathematical Society, 2001
Published in:
Transactions of the American Mathematical Society, 353 (2001) 9, Seite 3563-3583
Language:
English
ISSN:
0002-9947
Origination:
Footnote:
Description:
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.