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

2005 ◽  
Vol 33 (1) ◽  
pp. 244-299 ◽  
Author(s):  
Michael Eckhoff
Keyword(s):  
Precise Asymptotics ◽  
Small Eigenvalues

scholarly journals WITTEN DEFORMATION FOR NONCOMPACT MANIFOLDS WITH BOUNDED GEOMETRY

2021 ◽  
pp. 1-38
Author(s):  
Xianzhe Dai ◽  
Junrong Yan
Keyword(s):  
Essential Role ◽  
Morse Function ◽  
Noncompact Manifold ◽  
Morse Inequalities ◽  
Bounded Geometry ◽  
Noncompact Manifolds ◽  
Witten Laplacian ◽  
Relative Cohomology ◽  
Witten Deformation ◽  
Small Eigenvalues

Abstract Motivated by the Landau–Ginzburg model, we study the Witten deformation on a noncompact manifold with bounded geometry, together with some tameness condition on the growth of the Morse function f near infinity. We prove that the cohomology of the Witten deformation $d_{Tf}$ acting on the complex of smooth $L^2$ forms is isomorphic to the cohomology of the Thom–Smale complex of f as well as the relative cohomology of a certain pair $(M, U)$ for sufficiently large T. We establish an Agmon estimate for eigenforms of the Witten Laplacian which plays an essential role in identifying these cohomologies via Witten’s instanton complex, defined in terms of eigenspaces of the Witten Laplacian for small eigenvalues. As an application, we obtain the strong Morse inequalities in this setting.

Small eigenvalues on Riemann surfaces of genus 2

1991 ◽  
Vol 106 (1) ◽  
pp. 121-138 ◽  
Author(s):  
Paul Schmutz
Keyword(s):  
Riemann Surfaces ◽  
Genus 2 ◽  
Small Eigenvalues

Errata: Small Eigenvalues of Large Hankel Matrices

1968 ◽  
Vol 19 (6) ◽  
pp. 1508
Author(s):  
Harold Widom ◽  
Herbert Wilf
Keyword(s):  
Hankel Matrices ◽  
Small Eigenvalues

scholarly journals Precise Asymptotics in the Law of the Iterated Logarithm under Sublinear Expectations

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Mingzhou Xu ◽  
Kun Cheng
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Uniform Convergence ◽  
Central Limit ◽  
Random Variables ◽  
Precise Asymptotics ◽  
Partial Sum ◽  
The Central Limit Theorem ◽  
Iterated Logarithm ◽  
The Law

By an inequality of partial sum and uniform convergence of the central limit theorem under sublinear expectations, we establish precise asymptotics in the law of the iterated logarithm for independent and identically distributed random variables under sublinear expectations.

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