Geometric Characterization of the Eyring–Kramers Formula
Avelin, B., Julin, V., & Viitasaari, L. (2023). Geometric Characterization of the Eyring–Kramers Formula. Communications in Mathematical Physics, 404, 401-437. https://doi.org/10.1007/s00220-023-04845-z
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Communications in Mathematical PhysicsDate
2023Discipline
MatematiikkaAnalyysin ja dynamiikan tutkimuksen huippuyksikköMathematicsAnalysis and Dynamics Research (Centre of Excellence)Copyright
© The Author(s) 2023
In this paper we consider the mean transition time of an over-damped Brownian particle between local minima of a smooth potential. When the minima and saddles are non-degenerate this is in the low noise regime exactly characterized by the so called Eyring–Kramers law and gives the mean transition time as a quantity depending on the curvature of the minima and the saddle. In this paper we find an extension of the Eyring–Kramers law giving an upper bound on the mean transition time when both the minima/saddles are degenerate (flat) while at the same time covering multiple saddles at the same height. Our main contribution is a new sharp characterization of the capacity of two local minima as a ratio of two geometric quantities, i.e., the minimal cut and the geodesic distance.
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https://converis.jyu.fi/converis/portal/detail/Publication/188986345
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Research costs of Academy Research Fellow, AoFAdditional information about funding
Open access funding provided by Uppsala University. B.A. was supported by the Swedish Research Council dnr: 2019-04098. V.J. was supported by the Academy of Finland Grant 314227.License
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