Random Witten Laplacians: traces of semigroups, $L^2$-Betti numbers and index

Sergio Albeverio; Alexei Daletskii; Alexander Kalyuzhnyi

doi:10.4171/jems/123

JournalsjemsVol. 10, No. 3pp. 571–599

Random Witten Laplacians: traces of semigroups, $L^{2}$ -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

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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.

Cite this article

Sergio Albeverio, Alexei Daletskii, Alexander Kalyuzhnyi, Random Witten Laplacians: traces of semigroups, $L^{2}$ -Betti numbers and index. J. Eur. Math. Soc. 10 (2008), no. 3, pp. 571–599

DOI 10.4171/JEMS/123