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Low temperature
asymptotics for quasistationary distributions in a bounded
domain
Tony Lelièvre and Francis Nier |
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Vol. 8 (2015), No. 3, 561–628
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Abstract |
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We analyze the low temperature asymptotics of the quasistationary distribution associated with the overdamped Langevin dynamics (also known as 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 factors 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 widen the range of applicability, the usual assumption that the energy landscape is a Morse function has been relaxed as much as possible. |
Keywords
quasistationary distributions, Witten Laplacian, low
temperature asymptotics and semiclassical asymptotics
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Mathematical Subject Classification 2010
Primary: 58J10, 58J32, 60J65, 60J70, 81Q20
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Milestones
Received: 18 September 2013
Revised: 22 December 2014
Accepted: 18 February 2015
Published: 3 June 2015
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Authors |
| Tony Lelièvre | |
| CERMICS Université Paris-Est Joint Project-team INRIA Matherials 6 & 8 Avenue Blaise Pascal F-77455 Marne-la-Vallée France |
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| Francis Nier | |
| LAGA Université de Paris 13 UMR-CNRS 7539 Avenue Jean-Baptiste Clément F-93430 Villetaneuse France |
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