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Potential Analysis

, Volume 41, Issue 2, pp 517–541 | Cite as

Generalized Schrödinger Semigroups on Infinite Graphs

  • Batu Güneysu
  • Ognjen Milatovic
  • Françoise Truc
Article

Abstract

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

Feynman–Kac formula Infinite graph Markov process Schrödinger semigroup Vector bundle 

Mathematics Subject Classifications (2010)

39A12 47D08 

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Batu Güneysu
    • 1
  • Ognjen Milatovic
    • 2
  • Françoise Truc
    • 3
  1. 1.Institut für MathematikHumboldt-Universität zu BerlinBerlinGermany
  2. 2.Department of Mathematics and StatisticsUniversity of North FloridaJacksonvilleUSA
  3. 3.Institut FourierGrenoble UniversitySaint Martin d’Hères CedexFrance

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