Geodesic
On the behaviour of metrics $H_s$ on loop groups
Teoriâ slučajnyh processov, Tome 16 (2010) no. 1, pp. 39-43.

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The heat measures with respect to metric $H_s$ on loop groups were introduced by P. Malliavin; its behaviour as $s\downarrow 1/2$ of finite dimensional distributions was studied by Y. Inahama [J. Funct. Anal., 198 (2003), p. 311-340]. In this note, we shall transfer this problem to the long time behaviour of diffusion processes. We conclude the result by using a metric equivalent form for the lower bound of Ricci tensors.
Keywords: Loop groups, heat measures, metric $H_s$, Ricci tensor, Wasserstein distance. 
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Shizan Fang. On the behaviour of metrics $H_s$ on loop groups. Teoriâ slučajnyh processov, Tome 16 (2010) no. 1, pp. 39-43. http://geodesic.mathdoc.fr/item/THSP_2010_16_1_a4/

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