Note on basic features of large time behaviour of heat kernels

Journal
Journal für die reine und angewandte Mathematik  
Volume
2015
Issue
708
Start Page
73
End Page
95
Citation
Journal fur die Reine und Angewandte Mathematik 2015 (708): 73-95 (2015)
Publisher DOI
10.1515/crelle-2013-0070
Scopus ID
2-s2.0-84946824668
Publisher
De Gruyter
Large time behaviour of heat semigroups (and, more generally, of positive selfadjoint semigroups) is studied. Convergence of the semigroup to the ground state and of averaged logarithms of kernels to the ground state energy is shown in the general framework of positivity improving selfadjoint semigroups. This framework encompasses all irreducible semigroups coming from Dirichlet forms as well as suitable perturbations thereof. It includes, in particular, Laplacians on connected manifolds, metric graphs and discrete graphs.
DDC Class
510: Mathematik