Generalized Schrödinger semigroups on infinite graphs

Batu Gûneysu (1) , Ognjen Milatovic (2) , Francoise Truc (3)

1 Institut für Mathematik [Berlin]
2 UNF - University of North Florida [Jacksonville]
3 IF - Institut Fourier

With appropriate notions of Hermitian vector bundles and connections over weighted graphs which we allow to be locally infinite, we prove Feynman-Kac-type representations for the corresponding semigroups and derive several applications thereof.

Keywords: Markov process; vector bundles over weighted graphs; Feynman-Kac-type representations; covariant Schrödinger operators; Markov process .

Domains: Mathematical Physics [math-ph]; Functional Analysis [math.FA]; Probability [math.PR]

Batu Gûneysu, Ognjen Milatovic, Francoise Truc. Generalized Schrödinger semigroups on infinite graphs. Potential Analysis, 2014, 41 (2), pp.517-541. ⟨10.1007/s11118-013-9381-6⟩. ⟨hal-00838356⟩