Geodesic
Random Witten Laplacians: traces of semigroups, $L^2$-Betti numbers and index
Journal of the European Mathematical Society, Tome 10 (2008) no. 3, pp. 571-599 Cet article a éte moissonné depuis la source EMS Press

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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.
DOI : 10.4171/jems/123
Classification : 60-XX, 58-XX, 00-XX
Keywords: Witten Laplacian, infinite covering, von Neumann algebra, Betti numbers, Configuration space, Gibbs measure 
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     title = {Random {Witten} {Laplacians:} traces of semigroups, $L^2${-Betti} numbers and index},
     journal = {Journal of the European Mathematical Society},
     pages = {571--599},
     year = {2008},
     volume = {10},
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Sergio Albeverio; Alexei Daletskii; Alexander Kalyuzhnyi. Random Witten Laplacians: traces of semigroups, $L^2$-Betti numbers and index. Journal of the European Mathematical Society, Tome 10 (2008) no. 3, pp. 571-599. doi: 10.4171/jems/123

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