Let G be an infinite connected graph with uniformly bounded vertex degree, and let denote the Laplace operator corresponding to the simple random walk on it. In this paper we obtain relations between the structure of the graph and the qualitative behaviour of the class of functions u satisfying ub>0, namely we relate the asymptotic growth of the function u and that of the cardinality of balls in G.
Strongly subharmonic functions, graphs, and their asymptotic growth / M. Rigoli, M. Salvatori, M. Vignati. - In: MATHEMATISCHE ANNALEN. - ISSN 0025-5831. - 331:1(2005), pp. 21-39.
Strongly subharmonic functions, graphs, and their asymptotic growth
M. RigoliPrimo
;M. SalvatoriSecondo
;M. VignatiUltimo
2005
Abstract
Let G be an infinite connected graph with uniformly bounded vertex degree, and let denote the Laplace operator corresponding to the simple random walk on it. In this paper we obtain relations between the structure of the graph and the qualitative behaviour of the class of functions u satisfying ub>0, namely we relate the asymptotic growth of the function u and that of the cardinality of balls in G.
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