Abstract
Recent progress in the studying of the ergodicity problem of Markov semigroups on infinite dimensional spaces based on use of the hypercontractivity property is presented.
Supported by SFB 237
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Davies, E. B., Gross, L. and Simon, B., Hypercontractivity: A bibliographical review,in proceedings of the Hoegh—Krohn Memorial Conference.
Davies, E. B. and Simon, B., Ultracontractivity and the Heat Kernel for Schrödinger Operators and Dirichlet Laplacians, J. Func. Anal. 59 (1984), 335–395.
Gross, L., Logarithmic Sobolev inequalities, Amer. J. Math. 97 (1976), 1061–1083.
Holley, R. and Stroock, D. W., Logarithmic Sobolev inequalities and stochastic Ising models, J. Stat. Phys. 46 (1987), 1159–1194.
ShengLin, Lu, Horng-Tzer, Yau, Spectral Gap and Logarithmic Sobolev Inequality for Kawasaki and Glauber Dynamics, Preprint 1993.
Martinelli, F., Olivieri, E., Approach to Equilibrium of Glauber Dynamics in the One Phase Region: I. The Attractive case, II. The General Case,Preprints 1992/1993.
Rothaus, O. S., Logarithmic Sobolev Inequalities and the Spectrum of Schrödinger Operators, J. Func. Anal. 42 (1981), 110–378.
Simon, B., A remark on Nelson’s best hypercontractive estimates, Proc. AMS 55 (1976), 376–378.
Stroock, D. W. and Zegarlinski, B., The Logarithmic Sobolev Inequality for Continuous Spin Systems on a Lattice, J. Func. Anal. 104 (1992), 299–326.
Stroock, D. W. and Zegarlinski, B., The Equivalence of the Logarithmic Sobolev Inequality and the Dobrushin—Shlosman Mixing Condition,Commun. Math. Phys. 144(1992), 303323.
Stroock, D. W. and Zegarlinski, B., The Logarithmic Sobolev Inequality for Discrete Spin Systems on a Lattice, Commun. Math. Phys. 149 (1992), 175–193.
Stroock, D. W. and Zegarlinski, B., Some remarks about Glauber Dynamics and logarithmic Sobolev inequalities, MIT preprint 1993.
Zegarlinski, B., On log-Sobolev inequalities for infinite lattice systems, Lett. Math. Phys. 20 (1990), 173–182.
Zegarlinski, B., Log-Sobolev inequalities for infinite one-dimensional lattice systems,Comm. Math. Phys. 133(1990), 147–162.
Zegarlinski, B., Dobrushin uniqueness theorem and logarithmic Sobolev inequalities,J. Func. Anal. 105(1992), 77–111.
Zegarlinski, B., Strong exponential decay to equilibrium for the Markov hypercontractive semigroups associated to unbounded spin systems on a lattice,MIT Preprint 1992.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer Basel AG
About this paper
Cite this paper
Zegarlinski, B. (1995). Recent Progress in the Hypercontractive Semigroups. In: Bolthausen, E., Dozzi, M., Russo, F. (eds) Seminar on Stochastic Analysis, Random Fields and Applications. Progress in Probability, vol 36. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7026-9_19
Download citation
DOI: https://doi.org/10.1007/978-3-0348-7026-9_19
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-7028-3
Online ISBN: 978-3-0348-7026-9
eBook Packages: Springer Book Archive