Short-Time Asymptotics Of The Neumann Heat Kernel
Short-Time Asymptotics Of The Neumann Heat Kernel For Antipodal Points On The Exterior Of A Ball
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We use a probabilistic method to study the short-time asymptotic behavior of the heat kernel p(t; a; b) with the Neumann boundary condition in the exterior of an n-ball in the n-dimensional Euclidean Space when a and b are antipodal points. The asymptotic equivalence of the heat kernel p(t; a; b) is obtained by using the skew product of the reecting Brownian motion to reduce the problem to the computation of a Wiener functional on a Brownian bridge.
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