Title: Sharp laplace asymptotics in infinite dimensions
Other Titles: Scharfe Laplace Asymptotik in unendlicher Dimension
Language: English
Authors: Tempelmayr, Markus 
Qualification level: Diploma
Keywords: Laplace Asymptotik; Gaussmaße; Renormierung; Stochastische partielle Differentialgleichungen
Laplace asymptotics; Gaussian measures; renormalization; stochastic partial differential equations
Advisor: Beiglböck, Mathias 
Assisting Advisor: Di Gesu, Giacomo 
Issue Date: 2020
Number of Pages: 57
Qualification level: Diploma
In this thesis we study the sharp asymptotic behavior of perturbations of Gaussian measures on infinite dimensional spaces. We first introduce Gaussian measures on fractional Sobolev spaces over the d-dimensional torus. Depending on the space dimension d, these spaces are spaces of functions or distributions. We then construct some perturbations of Gaussian measures for d=1,2. In the case of d=1, the perturbation is constructed using the Sobolev embedding. For d=2, problems arise since the measure we are interested in can only be defined on spaces of distributions. We remedy this by what is called renormalization procedure in literature. Key steps are the hypercontractivity estimate for the Ornstein-Uhlenbeck semigroup and Nelson's estimate. We finally determine the sharp asymptotic behavior of the perturbations constructed.
URI: https://resolver.obvsg.at/urn:nbn:at:at-ubtuw:1-135885
Library ID: AC15618908
Organisation: E105 - Institut für Stochastik und Wirtschaftsmathematik 
Publication Type: Thesis
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