Metastability in Reversible Diffusion Processes I: Sharp Asymptotics for Capacities and Exit Times

By Anton Bovier, M. Eckhoff, V. Gayrard, M. Klein. 2004

399 citations recorded by the source corpus.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/d758e134fe662346a41c6e5be3c0ee76170ee240

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

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”
Generalisation of the Eyring–Kramers Transition Rate Formula to Irreversible Diffusion Processes (2015, methodology): “The mathematical proof of this formula, as well as its extension to more general metastable situations, was first obtained by Bovier, Eckhoff, Gayrard, and Klein [14] by means of a potential theoretic approach, and shortly after by Helffer, Klein and Nier [27] through Witten Laplacian analysis.”
A Hitting Time Analysis of Stochastic Gradient Langevin Dynamics (2017, methodology): “According to Bovier et al. [9], it takes the Langevin diffusion at least e Ω( ξh ) time to escape a depth-h basin of attraction.”
On the diffusion approximation of nonconvex stochastic gradient descent (2017, neutral): “The classical Eyring-Kramers formula [16] was first rigorously proved in [6, 28] and concludes as ε = √η → 0+ Ex∗τD = 2π |λ1(z∗)| √ | det(∇2F (z∗))| √ | det(∇2F (x∗))| exp ( F (z∗)− F (x∗) ε )( 1 +O ( ε1/2 log (1 ε ))) .”
Kramers' law: Validity, derivations and generalisations (2011, methodology): “1 ([5]).”
First exit times for Lévy-driven diffusions with exponentially light jumps. (2007, neutral): “WITH EXPONENTIALLY LIGHT JUMPS1 By Peter Imkeller, Ilya Pavlyukevich and Torsten Wetzel”
A Tail-Index Analysis of Stochastic Gradient Noise in Deep Neural Networks (2019, background): “These studies (Freidlin & Wentzell, 1998; Bovier et al., 2004; Imkeller et al., 2010b) consider the case where w0 is initialized in a”
Towards a Theory of Transition Paths (2006, background): “Equipped with Neumann boundary conditions on ∂!, (1) defines a strong Markov process with continuous path taking value in ! with reflection at the boundary.”
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.”
Geometric singular perturbation theory for stochastic differential equations (2002, result): “More detailed information on the asymptotics of the expected first-exit time has been obtained, see [2, 14] and the very precise results by Bovier, Eckhoff, Gayrard and Klein [8, 9] on the relation between the expected first-exit time, capacities and the spectrum of the generator of the diffusion.”
A Variational Approach to Modeling Slow Processes in Stochastic Dynamical Systems (2012, methodology): “4.2c and d, a nearly perfect approximation of both eigenvalues and eigenfunctions is obtained even though the number of basis functions used is identical to the MSM approach of the previous section.”
Metastability: A Potential-Theoretic Approach (2016, neutral): “The following result was proven in [6]:”