"Logarithmic Sobolev Inequalities for Free Loop Groups"  by Trevor Carson.

(UCSD Thesis, August 1997) )

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The manuscript is available as a DVI file (419K) or as a PDF file (977K).

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For a compact Lie group, $G$, let ${\cal L}(G)$ be the free loop group consisting of the space of continuous paths $g:[0,1]\rightarrow G$ with $ g(0)=g(1)$. For a given $Ad_{G}$-invariant inner product on the Lie algebra of $G$ and a suitable related inner product on the Lie algebra of ${\cal L}% (G)$ we derive the corresponding Riemannian structure on ${\cal L}(G)$. For this structure we have constructed finite dimensional approximations which are used in proving a logarithmic Sobolev inequality and integration by parts formulas on ${\cal L}(G)$. The underlying probability measure on $ {\cal L}(G)$ can be derived by an ${\cal L}(G)$-valued Brownian motion.

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July 15, 1998

08/15/2016 02:53 PM