Precise asymptotics of small eigenvalues of reversible diffusions in the metastable regime

DOI10.1214/009117904000000991zbMath1098.60079arXivmath/0503600OpenAlexW1994335347MaRDI QIDQ2497215

Michael Eckhoff

Publication date: 3 August 2006

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0503600

zbMATH Keywords

relaxation timepotential theorycapacitydiffusion processmetastabilitylarge deviationssemiclassical limitreversibilityexit problemPerron-Frobenius eigenvaluesground-state splittingWitten's Laplace

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Diffusion processes (60J60) Large deviations (60F10) Diffusion processes and stochastic analysis on manifolds (58J65) PDEs with randomness, stochastic partial differential equations (35R60) Harmonic, subharmonic, superharmonic functions on other spaces (31C05) Potentials and capacities on other spaces (31C15)

Related Items (13)

Finite Markov Chains Coupled to General Markov Processes and An Application to Metastability I ⋮ Finite Markov Chains Coupled to General Markov Processes and An Application to Metastability II ⋮ The tunneling effect for Schrödinger operators on a vector bundle ⋮ Metastable distributions of Markov chains with rare transitions ⋮ Full Metastable Asymptotic of the Fisher Information ⋮ Spectral analysis of discrete metastable diffusions ⋮ Tunneling for a class of difference operators: complete asymptotics ⋮ Metastability in a continuous mean-field model at low temperature and strong interaction ⋮ Sharp asymptotics of the first exit point density ⋮ Sharp tunneling estimates for a double-well model in infinite dimension ⋮ Simultaneous small noise limit for singularly perturbed slow-fast coupled diffusions ⋮ Asymptotic Behavior of the Principal Eigenvalue of a Linear Second Order Elliptic Operator with Small/Large Diffusion Coefficient ⋮ Effects of large degenerate advection and boundary conditions on the principal eigenvalue and its eigenfunction of a linear second order elliptic operator

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