Absence of spectral gaps on a class of loop spaces

DOI10.1016/S0021-7824(02)01260-6zbMath1029.58026MaRDI QIDQ1406917

Andreas Eberle

Publication date: 7 September 2003

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

zbMATH Keywords

Brownian bridgePoincaré inequalityno spectral gapLoop space

Mathematics Subject Classification ID

Loop spaces (55P35) Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds (58B20) Diffusion processes and stochastic analysis on manifolds (58J65) Stochastic calculus of variations and the Malliavin calculus (60H07)

Related Items (9)

Asymptotics of spectral gaps on loop spaces over a class of Riemannian manifolds ⋮ Log-Hessian and deviation bounds for Markov semi-groups, and regularization effect in \(\mathbb{L}^1 \) ⋮ Logarithmic heat kernel estimates without curvature restrictions ⋮ Local spectral gaps on loop spaces. ⋮ A concrete estimate for the weak Poincaré inequality on loop space ⋮ WITTEN LAPLACIAN ON PINNED PATH GROUP AND ITS EXPECTED SEMICLASSICAL BEHAVIOR ⋮ Spectral Gaps on Discretized Loop Spaces ⋮ Concentration of the Brownian bridge on Cartan-Hadamard manifolds with pinched negative sectional curvature. ⋮ A Poincaré inequality on loop spaces

Cites Work

• Integration by parts formulas and rotationally invariant Sobolev calculus on free loop spaces
• Large deviations and the Malliavin calculus
• Dirichlet forms and analysis on Wiener space
• Introduction to the theory of (non-symmetric) Dirichlet forms
• The log-Sobolev inequality on loop space over a compact Riemannian manifold
• Differential calculus on path and loop spaces. II: Irreducibility of Dirichlet forms on loop spaces
• Logarithmic Sobolev inequalities on path spaces over Riemannian manifolds
• Martingale representation and a simple proof of logarithmic Sobolev inequalities on path spaces
• Logarithmic derivatives of heat kernels and logarithmic Sobolev inequalities with unbounded diffusion coefficients on loop spaces
• Integration by parts for pinned Brownian motion
• A Cameron-Martin Type Quasi-Invariance Theorem for Pinned Brownian Motion on a Compact Riemannian Manifold
• Spectral gaps on loop spaces: a counterexample
• A class of integration by parts formulae in stochastic analysis I
• A geometric approach to on-diagonal heat kernel lower bounds on groups.
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