Metastability in reversible diffusion processes II. Precise asymptotics for small eigenvalues

By Anton Bovier, V. Gayrard, M. Klein. 2005

284 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e643480c344ad4ca25280aada28b9f315d40f2bc

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In Applied Mathematics

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Citations in the corpus

On hyperboundedness and spectrum of Markov operators (2014, background): “[33] and the references given therein), but they require more work and stronger hypotheses (assuming for instance that U is a Morse function).”
Metastability and Dominant Eigenvalues of Transfer Operators (2006, background): “Key words: Molecular dynamics, Markov processes, spectral properties, Rayleigh-trace, lower and upper bounds on metastability”
First exit times for Lévy-driven diffusions with exponentially light jumps. (2007, unknown): “WITH EXPONENTIALLY LIGHT JUMPS1 By Peter Imkeller, Ilya Pavlyukevich and Torsten Wetzel”
First exit times of SDEs driven by stable Lévy processes (2006, background): “Later on it was studied in [4–13], as well as in many other papers.”
Kramers' law: Validity, derivations and generalisations (2011, methodology): “Results in [5, 14] also include the following points: 1.”
A Tail-Index Analysis of Stochastic Gradient Noise in Deep Neural Networks (2019, background): “If the SDE (10) would be driven by the Brownian motion instead, then an analogous theorem to Theorem 2 holds saying that the transition times are still exponentially distributed but the scaling ε needs to be replaced by e 2 where H is the maximal depth of the basins to be traversed between the two l”
Precise Arrhenius Law for p-forms: The Witten Laplacian and Morse–Barannikov Complex (2011, methodology): “The accurate computations of its exponentially small eigenvalues has connections with various topics such as stochastic analysis ([6,7,14]), kinetic theory ([21,25–28]), the computation of geometric invariants ([3,4]), or differential topology ([8,31,38]).”
Non-convex learning via Stochastic Gradient Langevin Dynamics: a nonasymptotic analysis (2017, methodology): “Dalalyan and Tsybakov (2012) and Dalalyan (2016) analyzed rates of convergence of discretetime Langevin updates (with exact gradients) in the case of convex functions, and provided nonasymptotic rates of convergence in the total variation distance for sampling from log-concave densities. Durmus and ”
Metastability: A Potential-Theoretic Approach (2016, background): “The following result on the small eigenvalues of L is taken form [7]:”