Artículos de revistas
Ultrametric and Tree Potential
Fecha
2009Registro en:
J Theor Probab (2009) 22: 311–347
DOI 10.1007/s10959-009-0209-7
Autor
Dellacherie Lefebvre, Claude
San Martín Aristegui, Jaime
Martínez Aguilera, Servet
Institución
Resumen
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.