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5 votes
0 answers
242 views

Spectral gap for the Brownian motion with drift on a compact manifold

Let $M$ be a compact Riemannian manifold without boundary, $X$ a smooth vector field on $M$. Consider the Brownian motion $t\mapsto B_t$ on $M$ with drift $X$, so that its generator is $L=\Delta +X$. ...
Pierre PC's user avatar
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3 votes
1 answer
251 views

Feynman–Kac formula for other operators

I recently came across the Feynman-Kac formula which states that given an open domain $\Omega\in\mathbb{R}^n$ and $f \in L^2(\Omega)$ where $x \in \Omega$ and $t > 0$, then $e^{t\Delta_D}f(x) = ...
Emmie's user avatar
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