Logarithmic Sobolev inequalities on loop groups

DOI10.1016/0022-1236(91)90123-MzbMath0742.22003MaRDI QIDQ1180637

Publication date: 27 June 1992

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Brownian motion logarithmic Sobolev inequality compact connected Lie group space of paths Brownian bridge measure infinite dimensional loop group positivity-preserving hypercontractive semi-groups

Mathematics Subject Classification ID

Brownian motion (60J65) Analysis on real and complex Lie groups (22E30) Measures on groups and semigroups, etc. (43A05) Loop groups and related constructions, group-theoretic treatment (22E67)

Related Items (41)

Absolute continuity of heat kernel measure with pinned Wiener measure on loop groups ⋮ Couplings, gradient estimates and logarithmic Sobolev inequalitiy for Langevin bridges ⋮ Asymptotic behavior of divergences and Cameron-Martin theorem on loop spaces. ⋮ Rotations and quasi-invariance on the path space ⋮ A stochastic approach to the Euler-Poincaré number of the loop space of a developable orbifold ⋮ On forward stochastic integrals over the loop space ⋮ Martingale representation and logarithmic-Sobolev inequality for the fractional Ornstein-Uhlenbeck measure ⋮ De Rham-Hodge-Kodaira operator on loop groups ⋮ Logarithmic heat kernel estimates without curvature restrictions ⋮ On a certain semiclassical problem on Wiener spaces ⋮ Small-time Gaussian behavior of symmetric diffusion semigroups ⋮ A concrete estimate for the weak Poincaré inequality on loop space ⋮ Semi-classical limit of the bottom of spectrum of a Schrödinger operator on a path space over a compact Riemannian manifold ⋮ Integration on loop groups. II: Heat equation for the Wiener measure ⋮ Talagrand inequality on free path space and application to stochastic reaction diffusion equations ⋮ A Cameron-Martin Type Quasi-Invariance Theorem for Pinned Brownian Motion on a Compact Riemannian Manifold ⋮ A Cameron-Martin type quasi-invariance theorem for Brownian motion on a compact Riemannian manifold ⋮ WITTEN LAPLACIAN ON PINNED PATH GROUP AND ITS EXPECTED SEMICLASSICAL BEHAVIOR ⋮ Transportation cost inequalities on path and loop groups ⋮ Weak Poincaré inequalities on domains defined by Brownian rough paths ⋮ An estimate of the gap of spectrum of Schrödinger operators which generate hyperbounded semigroups ⋮ Poincaré inequality for weighted first order Sobolev spaces on loop spaces ⋮ GLAUBER DYNAMICS FOR QUANTUM LATTICE SYSTEMS ⋮ STOCHASTIC ADAMS THEOREM FOR A GENERAL COMPACT MANIFOLD ⋮ A STOCHASTIC APPROACH TO THE EULER–POINCARE CHARACTERISTIC OF A QUOTIENT OF A LOOP GROUP ⋮ Vanishing of one-dimensional \(L^2\)-cohomologies of loop groups ⋮ A Poincaré inequality on loop spaces ⋮ On Exponential Moments for Functionals Defined on the Loop Group ⋮ Integration by parts formula and logarithmic Sobolev inequality on the path space over loop groups ⋮ Preservation of log-Sobolev inequalities under some Hamiltonian flows ⋮ 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 derivatives of heat kernels and logarithmic Sobolev inequalities with unbounded diffusion coefficients on loop spaces ⋮ Singular Integral Homology of the Stochastic Loop Space ⋮ Riemannian distance, Rademacher theorem and transportation cost inequality on loop groups. ⋮ Stochastic gauge transform of the string bundle ⋮ Quasi-invariance for the pinned Brownian motion on a Lie group. ⋮ Hilbert Space of Spinor Fields Over the Free Loop Space ⋮ Stochastic Cohomology of the Frame Bundle of the Loop Space ⋮ Discussions on heat kernel measure and pinned Wiener measure

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