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New transience bounds for long walks in weighted digraphs
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Abstract
Fix two nodes i and j in an edge-weighted diagraph and form the following sequence: Let a ( n ) be the maximum weight of walks from i to j of length n ; if no such walk exists, a ( n ) = −∞. It is known that, if G is strongly connected, the sequence a(n) is always eventually periodic with linear defect, i.e. , after the transient , a ( n + p ) = a ( n ) + p · λ. In fact, the ratio λ is the largest mean weight of cycles in G . We call these cycles critical . Periodicity stems from the fact that the weights of critical cycles eventually dominate the maximum weight walks.
@misc{charronbost2013transience,
title = {New transience bounds for long walks in weighted digraphs},
author = {Bernadette Charron-Bost and Matthias Függer and Thomas Nowak},
year = {2013},
pages = {623--624},
doi = {10.1007/978-88-7642-475-5_103},
}