JournalsjemsVol. 10 , No. 3DOI 10.4171/jems/123

Random Witten Laplacians: traces of semigroups, <em>L<sup>2</sup></em>-Betti numbers and index

  • Sergio Albeverio

    Universität Bonn, Germany
  • Alexei Daletskii

    Nottingham Trent University, United Kingdom
  • Alexander Kalyuzhnyi

    National Academy of Science of Ukraine, Kyiv, Ukraine
Random Witten Laplacians: traces of semigroups, <em>L<sup>2</sup></em>-Betti numbers and index cover

Abstract

Random Witten Laplacians on infinite coverings of compact manifolds are considered. The probabilistic representations of the corresponding heat kernels are given. The finiteness of the von Neumann traces of the corresponding semigroups is proved, and the short-time asymptotics of the corresponding super-trace is computed. Examples associated with Gibbs measures on configuration spaces and product manifolds are considered.