Ultrametric and Tree Potential |
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Authors: | Claude Dellacherie Servet Martinez Jaime San Martin |
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Institution: | 1. Laboratoire Rapha?l Salem, UMR 6085, Université de Rouen, Site Colbert, 76821, Mont Saint Aignan Cedex, France 2. CMM-DIM; UMI 2807 CNRS-UCHILE, FCFM, Universidad de Chile, Casilla 170-3 Correo 3, Santiago, Chile
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Abstract: | In this article we study which infinite matrices are potential matrices. We tackle this problem in the ultrametric framework
by studying infinite tree matrices and ultrametric matrices. For each tree matrix, we show the existence of an associated
symmetric random walk and study its Green potential. We provide a representation theorem for harmonic functions that includes
simple expressions for any increasing harmonic function and the Martin kernel. For ultrametric matrices, we supply probabilistic
conditions to study its potential properties when immersed in its minimal tree matrix extension.
C. Dellacherie thanks support from Nucleus Millennium P04-069-F for his visit to CMM-DIM at Santiago.
The research of S. Martinez is supported by Nucleus Millennium Information and Randomness P04-069-F and by the BASAL CONICYT
Program.
The research of J. San Martin is supported by FONDAP and by the BASAL CONICYT Program. |
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Keywords: | Potential theory Ultrametricity Harmonic functions Martin kernel |
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