Minimal volume entropy for graphs

Lim, Seonhee

doi:10.1090/S0002-9947-08-04227-X

Minimal volume entropy for graphs
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Trans. Amer. Math. Soc. 360 (2008), 5089-5100 Request permission

Abstract:

Among the normalized metrics on a graph, we show the existence and the uniqueness of an entropy-minimizing metric, and give explicit formulas for the minimal volume entropy and the metric realizing it.

Parmi les distances normalisées sur un graphe, nous montrons l’existence et l’unicité d’une distance qui minimise l’entropie, et nous donnons des formules explicites pour l’entropie volumique minimale et la distance qui la réalise.

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