Mathematische Annalen

, Volume 331, Issue 1, pp 21–39 | Cite as

Strongly subharmonic functions, graphs, and their asymptotic growth

  • Marco Rigoli
  • Maura Salvatori
  • Marco VignatiEmail author


Let G be an infinite connected graph with uniformly bounded vertex degree, and let Δ 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 Δub>0, namely we relate the asymptotic growth of the function u and that of the cardinality of balls in G.


Random Walk Laplace Operator Connected Graph Qualitative Behaviour Vertex Degree 
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© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Dipartimento di Scienze Chimiche, Matematiche e FisicheUniversità dell’InsubriaComoItaly
  2. 2.Dipartimento di MatematicaUniversità di MilanoMilanoItaly
  3. 3.Dipartimento di MatematicaUniversità di MilanoMilanoItaly

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