
"Logarithmic Sobolev Inequalities for Free Loop Groups" by Trevor Carson.(UCSD Thesis, August 1997) )
The manuscript is available as a DVI file (419K) or as a PDF file (977K). Abstract 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.
July 15, 1998 
08/15/2016 02:53 PM 