Logarithmic Sobolev inequalities for infinite dimensional Hörmander type generators on the Heisenberg group

DOI10.1007/s11118-009-9126-8zbMath1180.22012arXiv0901.1765OpenAlexW3103861646WikidataQ105583431 ScholiaQ105583431MaRDI QIDQ2391051

Ioannis Papageorgiou, James D. Inglis

Publication date: 24 July 2009

Published in: Potential Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0901.1765

zbMATH Keywords

Heisenberg grouplogarithmic Sobolev inequalityGibbs measuresHörmander type generators

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Analysis on real and complex Lie groups (22E30) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Diffusion processes and stochastic analysis on manifolds (58J65) Functional inequalities, including subadditivity, convexity, etc. (39B62) Inequalities involving derivatives and differential and integral operators (26D10)

Related Items (13)

Markov semigroups with hypocoercive-type generator in infinite dimensions: ergodicity and smoothing ⋮ Linear and nonlinear dissipative dynamics ⋮ Solution of a class of reaction-diffusion systems via logarithmic Sobolev inequality ⋮ From \(U\)-bounds to isoperimetry with applications to H-type groups ⋮ The log-Sobolev inequality with quadratic interactions ⋮ Long- and short-time behaviour of hypocoercive-type operators in infinite dimensions: An analytic approach ⋮ \(q\)-Poincaré inequalities on Carnot groups with filiform type Lie algebra ⋮ A note on the modified log-Sobolev inequality ⋮ CONCENTRATION INEQUALITIES FOR GIBBS MEASURES ⋮ Functional inequalities and Hamilton-Jacobi equations in geodesic spaces ⋮ Ergodicity of Markov semigroups with Hörmander type generators in infinite dimensions ⋮ Log-Sobolev inequalities for subelliptic operators satisfying a generalized curvature dimension inequality ⋮ An L2-approximation method for construction and smoothing estimates of Markov semigroups for interacting diffusion processes on a lattice

Cites Work

• A new criterion for the logarithmic Sobolev inequality and two applications
• On gradient bounds for the heat kernel on the Heisenberg group
• Analytic inequalities, isoperimetric inequalities and logarithmic Sobolev inequalities
• The logarithmic Sobolev inequality for continuous spin systems on a lattice
• The log-Sobolev inequality for unbounded spin systems
• Application of log-Sobolev inequality to the stochastic dynamics of unbounded spin systems on the lattice
• Hamilton-Jacobi theory and the heat kernel on Heisenberg groups
• From Brunn-Minkowski to Brascamp-Lieb and to logarithmic Sobolev inequalities
• The strong decay to equilibrium for the stochastic dynamics of unbounded spin systems on a lattice
• Coercive inequalities for Hörmander type generators in infinite dimensions
• Estimation optimale du gradient du semi-groupe de la chaleur sur le groupe de Heisenberg
• Some properties of Carnot-Carath'eodory balls in the Heisenberg group
• On log-Sobolev inequalities for infinite lattice systems
• Stratified Lie Groups and Potential Theory for their Sub-Laplacians
• Logarithmic Sobolev Inequalities
• Séminaire de Probabilités XXXVI
• Entropy bounds and isoperimetry
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Logarithmic Sobolev inequalities for infinite dimensional Hörmander type generators on the Heisenberg group