Laplace's method for the laws of heat processes on loop spaces |
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Authors: | Yuzuru Inahama |
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Affiliation: | Department of Mathematical Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan |
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Abstract: | In this paper, we will consider Laplace's method for a class of heat processes on loop spaces. We will obtain the first term of the asymptotics under assumptions that the function under consideration attains its minimum at a unique point and that the Hessian at the point is non-degenerate. This kind of process was first introduced by P. Malliavin in 1990 for the loop group case and then gradually generalized by various authors. Our tool is the rough path theory of T. Lyons. This technique was pioneered by S. Aida for finite-dimensional processes in his unpublished paper. |
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Keywords: | Laplace's method Rough path theory Loop space Heat process |
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