A concrete estimate for the weak Poincaré inequality on loop space

DOI10.1007/s00440-010-0308-5zbMath1245.58017arXiv0910.4846OpenAlexW3102226638MaRDI QIDQ662822

Xin Chen, Xue-Mei Li, Bo Wu

Publication date: 13 February 2012

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0910.4846

zbMATH Keywords

Ornstein-Uhlenbeck operatorloop spaceweak Poincaré inequalityBrownian bridge measure

Mathematics Subject Classification ID

Applications of stochastic analysis (to PDEs, etc.) (60H30) Diffusion processes and stochastic analysis on manifolds (58J65)

Related Items (5)

On the characterization of Brownian bridge measure on the pinned path space over a compact Riemannian manifold ⋮ Asymptotics of spectral gaps on loop spaces over a class of Riemannian manifolds ⋮ Stochastic Heat Equations with Values in a Manifold via Dirichlet Forms ⋮ Logarithmic heat kernel estimates without curvature restrictions ⋮ Stochastic heat equations for infinite strings with values in a manifold

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Short time behavior of the heat kernel and its logarithmic deviatives
• Asymptotics of the spectral gap with applications to the theory of simulated annealing
• A Poincaré inequality on loop spaces
• Logarithmic Sobolev inequalities on loop groups
• Analysis on Wiener spaces. II: Differential forms
• The log-Sobolev inequality on loop space over a compact Riemannian manifold
• Uniform positivity improving property, Sobolev inequalities, and spectral gaps
• 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
• Absence of spectral gaps on a class of loop spaces
• Local spectral gaps on loop spaces.
• Logarithmic derivatives of heat kernels and logarithmic Sobolev inequalities with unbounded diffusion coefficients on loop spaces
• On the geometry of diffusion operators and stochastic flows
• Spectral Gaps on Discretized Loop Spaces
• A Cameron-Martin Type Quasi-Invariance Theorem for Pinned Brownian Motion on a Compact Riemannian Manifold
• Diffusion processes in a small time interval
• A class of integration by parts formulae in stochastic analysis I
• An estimate of the gap of spectrum of Schrödinger operators which generate hyperbounded semigroups
• Weak Poincaré inequalities and \(L^2\)-convergence rates of Markov semigroups

This page was built for publication: A concrete estimate for the weak Poincaré inequality on loop space