@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}
}
@article{KellerLenzSchmidtetal.2019,
  author    = {Keller, Matthias and Lenz, Daniel and Schmidt, Marcel and Schwarz, Michael},
  title     = {Boundary representation of Dirichlet forms on discrete spaces},
  series = {Journal de Math{\´e}matiques Pures et Appliqu{\´e}es},
  volume    = {126},
  journal   = {Journal de Math{\´e}matiques Pures et Appliqu{\´e}es},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0021-7824},
  doi       = {10.1016/j.matpur.2018.10.005},
  pages     = {109 -- 143},
  year      = {2019},
  abstract  = {We describe the set of all Dirichlet forms associated to a given infinite graph in terms of Dirichlet forms on its Royden boundary. Our approach is purely analytical and uses form methods. (C) 2018 Elsevier Masson SAS.},
  language  = {en}
}