### ON THE BEHAVIOUR OF METRICS $H_s$ ON LOOP GROUPS

**SHIZAN FANG**

*Theory of Stochastic Processes*

*Vol.16 (32), no.1, 2010, pp.39-43*

The heat measures with respect to metric Hs on loop groups were introduced by P. Malliavin; its behaviour as s ↓ 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.