Author : Richard Bucher Sowers
Publisher : Oxford University Press, USA
Page : 145 pages
File Size : 45,9 Mb
Release : 2014-09-11
Category : Filters
ISBN : 1470402181
Short-Time Geometry of Random Heat Kernels by Richard Bucher Sowers Pdf
This volume studies the behaviour of a random heat kernel associated with a stochastic partial differential equation, and gives short-time expansion of this heat kernel. The author finds that the dominant exponential term is classical and depends only on the Riemannian distance function. The second exponential term is a work term and also has classical meaning. There is also a third non-negligible exponential term which blows up. The author finds an expression for this third exponential term which involves a random translation of the index form and the equations of Jacobi fields. In the process, he develops a method to approximate the heat kernel to any arbitrary degree of precision.