Sharp spectral asymptotics for non-reversible metastable diffusion processes

D. Le Peutrec and B. Nectoux, Small eigenvalues of the Witten Laplacian with Dirichlet boundary conditions: the case with critical points on the boundary , 2019, to appear in Ann. PDE, preprint available on https://arxiv.org/abs/1907.07517 , 63 pages

Original

1907

Earlier work this paper cites.

T. Kato, Perturbation theory for linear operators , Classics in Mathematics, Springer-Verlag, Berlin, 1995, Reprint of the 1980 edition

1980

Earlier work this paper cites.

E. Witten, Supersymmetry and Morse theory , J. Differential Geom. 17

1983

Earlier work this paper cites.

B. Helffer and J. Sjöstrand, Puits multiples en mécanique semi-classique. IV. Étude du complexe de Witten , Comm. Partial Differential Equations 10

1985

Earlier work this paper cites.

B. Helffer, Semi-classical analysis for the Schrödinger operator and applications , Lecture Notes in Mathematics, vol. 1336, Springer-Verlag, 1988

1988

Earlier work this paper cites.

A. Bovier, M. Eckhoff, V. Gayrard, and M. Klein, Metastability in reversible diffusion processes. I. Sharp asymptotics for capacities and exit times , J. Eur. Math. Soc. 6

2004

Earlier work this paper cites.

B. Helffer, M. Klein, and F. Nier, Quantitative analysis of metastability in reversible diffusion processes via a Witten complex approach , Mat. Contemp. 26

2004

Earlier work this paper cites.

A. Bovier, V. Gayrard, and M. Klein, Metastability in reversible diffusion processes. II. Precise asymptotics for small eigenvalues , J. Eur. Math. Soc. 7

2005

Earlier work this paper cites.

B. Helffer and F. Nier, Hypoelliptic estimates and spectral theory for Fokker-Planck operators and Witten Laplacians , Lecture Notes in Mathematics, vol. 1862, Springer-Verlag, Berlin, 2005

2005

Cited alongside, same era.

by same author, Quantitative analysis of metastability in reversible diffusion processes via a Witten complex approach: the case with boundary , Mém. Soc. Math. Fr. (N.S.) (2006), no. 105

2006

Cited alongside, same era.

D. Le Peutrec, Small eigenvalues of the Neumann realization of the semiclassical Witten Laplacian , Ann. Fac. Sci. Toulouse Math. (6) 19

2010

Cited alongside, same era.

F. Hérau, M. Hitrik, and J. Sjöstrand, Tunnel effect and symmetries for Kramers-Fokker-Planck type operators , J. Inst. Math. Jussieu 10

2011

Cited alongside, same era.

by same author, Spectral theory and its applications , vol. 139, Cambridge University Press, 2013

L. Michel, Around supersymmetry for semiclassical second order differential operators , Proc. Amer. Math. Soc. 144

2016

Later among the works it cites.

G. Di Gesù and D. Le Peutrec, Small noise spectral gap asymptotics for a large system of nonlinear diffusions , J. Spectr. Theory 7

2017

Later among the works it cites.

C. Landim and I. Seo, Metastability of nonreversible random walks in a potential field and the Eyring-Kramers transition rate formula , Comm. Pure Appl. Math. 71

2018

Later among the works it cites.

L. Michel and M. Zworski, A semiclassical approach to the Kramers-Smoluchowski equation , SIAM J. Math. Anal. 50

2018

Later among the works it cites.

C. Landim, M. Mariani, and I. Seo, Dirichlet’s and Thomson’s principles for non-selfadjoint elliptic operators with application to non-reversible metastable diffusion processes , Arch. Rational Mech. Anal. 231