Mathematische Zeitschrift

, Volume 274, Issue 3, pp 905-932

First online:

Volume growth, spectrum and stochastic completeness of infinite graphs

  • Matthias KellerAffiliated withMathematisches Institut, Friedrich Schiller Universität Jena
  • , Daniel LenzAffiliated withMathematisches Institut, Friedrich Schiller Universität Jena
  • , Radosław K. WojciechowskiAffiliated withYork College of the City University of New York Email author 

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


We study the connections between volume growth, spectral properties and stochastic completeness of locally finite weighted graphs. For a class of graphs with a very weak spherical symmetry we give a condition which implies both stochastic incompleteness and discreteness of the spectrum. We then use these graphs to give some comparison results for both stochastic completeness and estimates on the bottom of the spectrum for general locally finite weighted graphs.

Mathematics Subject Classification (2000)

Primary 39A12 Secondary 58J35