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Metastable diffusions with degenerate drifts
- Publication Year :
- 2022
-
Abstract
- We study the spectrum of the semiclassical Witten Laplacian $\Delta_{f}$ associated to a smooth function $f$ on ${\mathbb R}^d$. We assume that $f$ is a confining Morse--Bott function. Under this assumption we show that $\Delta_{f}$ admits exponentially small eigenvalues separated from the rest of the spectrum. Moreover, we establish Eyring-Kramers formula for these eigenvalues. Our approach is based on microlocal constructions of quasimodes near the critical submanifolds.<br />Comment: 28 pages, 6 figures
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2202.02208
- Document Type :
- Working Paper