Abstract
We use the Feynman-Kac formula and a decomposition of the Brownian bridge to obtain pointwise estimates on the diagonal elements of the heat kernel. We also compute bounds on trace ( e tΔ D ) where Δ D is the Dirichlet Laplacian for (i) a bounded region D in R n with smooth boundary or (ii) an unbounded region D in R 2 with finite area.
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