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Note on short‐time behavior of semigroups associated to self‐adjoint operators
Author(s) -
Keller Matthias,
Lenz Daniel,
Münch Florentin,
Schmidt Marcel,
Telcs András
Publication year - 2016
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdw054
Subject(s) - mathematics , heat kernel , bounded function , simple (philosophy) , graph , kernel (algebra) , pure mathematics , self adjoint operator , type (biology) , discrete mathematics , combinatorics , mathematical analysis , hilbert space , ecology , biology , philosophy , epistemology
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.