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We analyze the low temperature asymptotics of the quasi-stationary distribution associated with the overdamped Langevin dynamics (a.k.a. the Einstein-Smoluchowski diffusion equation) in a bounded domain. This analysis is useful to rigorously prove the consistency of an algorithm used in molecular dynamics (the hyperdynamics), in the small temperature regime. More precisely, we show that the algorithm is exact in terms of state-to-state dynamics up to exponentially small factor in the limit of small temperature. The proof is based on the asymptotic spectral analysis of associated Dirichlet and Neumann realizations of Witten Laplacians. In order to cover a reasonably large range of applications, the usual assumptions that the energy landscape is a Morse function has been relaxed as much as possible.
Suppose that $X$ is a subcritical superprocess. Under some asymptotic conditions on the mean semigroup of $X$, we prove the Yaglom limit of $X$ exists and identify all quasi-stationary distributions of $X$.
This article is mainly devoted to the asymptotic analysis of a fractional version of the (elliptic) Allen-Cahn equation in a bounded domain $Omegasubsetmathbb{R}^n$, with or without a source term in the right hand side of the equation (commonly calle
A hyperbolic relaxation of the classical Navier-Stokes problem in 2D bounded domain with Dirichlet boundary conditions is considered. It is proved that this relaxed problem possesses a global strong solution if the relaxation parameter is small and t
Quasi-stationary distributions (QSDs)arise from stochastic processes that exhibit transient equilibrium behaviour on the way to absorption QSDs are often mathematically intractable and even drawing samples from them is not straightforward. In this pa
Wang and Ye conjectured in [22]: Let $Omega$ be a regular, bounded and convex domain in $mathbb{R}^{2}$. There exists a finite constant $C({Omega})>0$ such that [ int_{Omega}e^{frac{4pi u^{2}}{H_{d}(u)}}dxdyle C(Omega),;;forall uin C^{infty}_{0}(Om