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SUMMARY:Seonhee Lim (Seoul National University)
DTSTART:20210614T080000Z
DTEND:20210614T091500Z
DTSTAMP:20260423T053016Z
UID:BODS/18
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/BODS/18/">Br
 ownian motion in negative curvature</a>\nby Seonhee Lim (Seoul National Un
 iversity) as part of Bremen Online Dynamics Seminar\n\n\nAbstract\nBrownia
 n motion in the hyperbolic space $H^n$ is rather\nwell-known with a precis
 e formula for the heat kernel\, which is the\nprobability density function
  of the Brownian motion. In this talk\, we\nwill talk about the asymptotic
  formula for the heat kernel in a\nconnected simply connected negatively c
 urved Riemannian manifold X whose\nmetric is lifted from a compact manifol
 d M.\n As time goes to infinity\, we show that the heat kernel $p(t\,x\,y)
 $ is\nasymptotically $e^{-\\lambda_0} t^{-3/2} C(x\,y)$ where $\\lambda_0$
  is the\nbottom of the spectrum of the geometric Laplacian. The proof uses
  the\nuniform Harnack inequality on the boundary $\\partial X$ as well as 
 the\nuniform mixing of the geodesic flow on the quotient manifold M. (This
  is\na joint work with François Ledrappier.)\n
LOCATION:https://researchseminars.org/talk/BODS/18/
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