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| This talk will be about the precise computation of the first non zero eigenvalue of some semi-classical positive Schroedinger operator, the Witten Laplacian, at the semi-classical limit $h\to 0$, in large dimension.
These operators are distorted semi-classical Laplacians by means of a Morse function $f$. The study of their low spectrum at the semi-classical limit is closely related to the study of the metastability for the overdamped Langevin processes $d X_t = -\nabla f (X_t) + \sqrt{2h} d W_t $.
In this talk, we will look at the Witten Laplacian associated with a particular Morse function corresponding
to some coupled bistable system, in large dimension. |
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