Modulus of families of walks on graphs

Faryad Darabi Sahneh; Max Goering; Nathan Albin; Pietro Poggi-Corradini

Modulus of families of walks on graphs

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arxiv 1401.7640 v3 pith:265NS4OS submitted 2014-01-29 math.CO math.CV

Nathan Albin , Pietro Poggi-Corradini , Faryad Darabi Sahneh , Max Goering This is my paper

classification math.COmath.CV

keywords graphsmodulusbeurlingcriterionfamilieswalksalgorithmcase

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We introduce the notion of modulus of families of walks on graphs. We show how Beurling's famous criterion for extremality, that was formulated in the continuous case, can be interpreted on graphs as an instance of the Karush-Kuhn-Tucker conditions. We then develop an algorithm to numerically compute modulus using Beurling's criterion as our guide.

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$p$-Modulus on radially symmetric trees
math.CO 2025-06 conditional novelty 6.0 of 10

For infinite radially symmetric trees, the p-modulus of all root-to-infinity paths is (sum_k (sigma_k |S_k|)^{-q/p})^{-p/q}, and a critical p-value separates positive from zero modulus.

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