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- W3006407179 abstract "Let $f: mathbb R^{d} to mathbb R$ be a smooth function, and let $(X_t)_{tge 0}$ be the stochastic process solution to the overdamped Langevin dynamics $d X_t = -nabla f(X_t) d t + sqrt{h} d B_t$. Let $Omegasubset mathbb R^d$ be a smooth bounded domain, and assume that $f|_{overlineOmega}$ is a double-well potential with degenerate barriers. In this work, we study in the small temperature regime, i.e., when $hto 0^{+}$, the asymptotic repartition of the quasi-stationary distribution of $(X_t)_{tge 0}$ in $Omega$ within the two wells of $f|_{overlineOmega}$. We show that this distribution generically concentrates in precisely one well of $f|_{overlineOmega}$ when $hto 0^{+}$ but can nevertheless concentrate in both wells when $f|_{overlineOmega}$ admits sufficient symmetries. This phenomenon corresponds to the so-called tunneling effect in semiclassical analysis. We also investigate in this setting the asymptotic behavior when $hto 0^{+}$ of the first exit point distribution from $Omega$ of $(X_t)_{tge 0}$ when $X_0$ is distributed according to the quasi-stationary distribution." @default.
- W3006407179 created "2020-02-24" @default.
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- W3006407179 date "2020-01-01" @default.
- W3006407179 modified "2023-09-26" @default.
- W3006407179 title "Repartition of the Quasi-stationary Distribution and First Exit Point Density for a Double-Well Potential" @default.
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- W3006407179 doi "https://doi.org/10.1137/19m1246432" @default.
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