๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Asymptotics of Heat Kernels on Projective Spaces of Large Dimensions and on Disk Hypergroups

โœ Scribed by Michael Voit

Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
597 KB
Volume
194
Category
Article
ISSN
0025-584X

No coin nor oath required. For personal study only.

โœฆ Synopsis

In this note we give exact asymptotic rates of convergence of Brownian motions on complex and quaternionic projective spacea to the uniform distribution when the dimension of these tipii~m tends to infinity. Similar results are ah0 established for the symmetric spacea U(n)/U(n -1) and disk hypergroups. Proofs will be based on a comparision of heat kernels with Poisson kernels together with a central limit result for Poisson kernels.

X, starting in 3: at time 0. It is well-known that Brownian motions on X , tend in distribution to U, for t + 00, and it is natural to ask for quantitative estimates on how ht,, tends to 1 depending on n. Such problems of convergence to equilibrium

๐Ÿ“œ SIMILAR VOLUMES

Asymptotic Behavior of Heat Kernels on S
Asymptotic Behavior of Heat Kernels on Spheres of Large Dimensions
โœ Michael Voit ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 679 KB

For n 2, let (+ x {, n ) { 0 be the distributions of the Brownian motion on the unit sphere S n /R n+1 starting in some point x # S n . This paper supplements results of Saloff-Coste concerning the rate of convergence of + x {, n to the uniform distribution U n on S n for { ร„ depending on the dimens

Logarithmic Derivatives of Heat Kernels
Logarithmic Derivatives of Heat Kernels and Logarithmic Sobolev Inequalities with Unbounded Diffusion Coefficients on Loop Spaces
โœ Shigeki Aida ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 294 KB

dedicated to professor norio shimakura on the occasion of his sixtieth birthday In this paper, we will give a sufficient condition on the logarithmic derivative of the heat kernel under which a logarithmic Sobolev inequality (LSI, in abbreviation) on a loop space holds. As an application, we prove