Note on short‐time behavior of semigroups associated to self‐adjoint operators. (3rd November 2016)

• Record Type: Journal Article
• Authors: Keller, Matthias; Lenz, Daniel; Münch, Florentin; Schmidt, Marcel; Telcs, András
• Is Part Of: Bulletin of the London Mathematical Society. Volume 48:Part 6(2016:Dec.)
• Page Start: 935
• Page End: 944
• Publication Date: 2016-11-03
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1112/blms/bdw054
• Languages: English
• ISSNs: 0024-6093

Abstract

Abstract : We present a simple observation showing that the heat kernel on a locally finite graph behaves for short timest roughly liket d, whered 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.