HYPERCONTRACTIVITY VIA SPECTRAL THEORY

DOI10.1142/S0219025700000030zbMath1040.47503WikidataQ130116377 ScholiaQ130116377MaRDI QIDQ4430257

Thierry Bodineau, Bogusław Zegarliński

Publication date: 16 December 2003

Published in: Infinite Dimensional Analysis, Quantum Probability and Related Topics (Search for Journal in Brave)

zbMATH Keywords

stochastic dynamicsspectral theorydiscrete spectrumspectral representationhypercontractivityone-dimensional Ising modelsymmetric Markov semigroupnearest neighbours interactioninfinite-dimensional modelsnon-commutative spin systems

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Markov semigroups and applications to diffusion processes (47D07) Groups and semigroups of linear operators (47D03) Quantum equilibrium statistical mechanics (general) (82B10) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Related Items (10)

Linear and nonlinear dissipative dynamics ⋮ OPTIMAL LOG-SOBOLEV INEQUALITY AND HYPERCONTRACTIVITY FOR POSITIVE SEMIGROUPS ON $M_2({\mathbb C})$ ⋮ Spectral Properties of Circulant Quantum Markov Semigroups ⋮ Super Poincaré inequalities, Orlicz norms and essential spectrum ⋮ Exponential decay of matrix Φ-entropies on Markov semigroups with applications to dynamical evolutions of quantum ensembles ⋮ Matrix Poincaré, Φ-Sobolev inequalities, and quantum ensembles ⋮ Hypercontractivity for a quantum Ornstein-Uhlenbeck semigroup ⋮ Entropy production of doubly stochastic quantum channels ⋮ Logarithmic Sobolev inequalities in non-commutative algebras ⋮ Stability of local quantum dissipative systems

Cites Work

• Log-Sobolev inequalities for infinite one-dimensional lattice systems
• Hypercontractivity in noncommutative \(L_1\) spaces
• Logarithmic Sobolev Inequalities

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