@article{KellerMuenchPogorzelski2016,
  author    = {Keller, Matthias and M{\"u}nch, Florentin and Pogorzelski, Felix},
  title     = {Geometry and spectrum of rapidly branching graphs},
  series = {Mathematische Nachrichten},
  volume    = {289},
  journal   = {Mathematische Nachrichten},
  publisher = {Wiley-VCH},
  address   = {Weinheim},
  issn      = {0025-584X},
  doi       = {10.1002/mana.201400349},
  pages     = {1636 -- 1647},
  year      = {2016},
  abstract  = {We study graphs whose vertex degree tends to infinity and which are, therefore, called rapidly branching. We prove spectral estimates, discreteness of spectrum, first order eigenvalue and Weyl asymptotics solely in terms of the vertex degree growth. The underlying techniques are estimates on the isoperimetric constant. Furthermore, we give lower volume growth bounds and we provide a new criterion for stochastic incompleteness. (C) 2016 WILEY-VCH Verlag GmbH \& Co. KGaA, Weinheim},
  language  = {en}
}
@article{KellerLenzMuenchetal.2016,
  author    = {Keller, Matthias and Lenz, Daniel and M{\"u}nch, Florentin and Schmidt, Marcel and Telcs, Andras},
  title     = {Note on short-time behavior of semigroups associated to self-adjoint operators},
  series = {Bulletin of the London Mathematical Society},
  volume    = {48},
  journal   = {Bulletin of the London Mathematical Society},
  publisher = {Oxford Univ. Press},
  address   = {Oxford},
  issn      = {0024-6093},
  doi       = {10.1112/blms/bdw054},
  pages     = {935 -- 944},
  year      = {2016},
  abstract  = {We present a simple observation showing that the heat kernel on a locally finite graph behaves for short times t roughly like t(d), where d is the combinatorial distance. This is very different from the classical Varadhan-type behavior on manifolds. Moreover, this also gives that short-time behavior and global behavior of the heat kernel are governed by two different metrics whenever the degree of the graph is not uniformly bounded.},
  language  = {en}
}