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Showing 1 to 4 of 4 for “"Logarithmic Sobolev inequality"”.
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Functional inequalities in quantum information theory
… nature of such processes. The first logarithmic Sobolev inequality to be proved, due to Gross, was for the Ornstein Uhlenbeck semigroup, that is the Brownian motion with friction on the real line. The generalization of this result to the quantum Ornstein Uhlenbeck semigroup was found …
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Intrinsic Ultracontractivity and Other Properties of Mixed Barrier Brownian Motions
… state of H on D with mixed boundary conditions. Logarithmic Sobolev inequality and the theory of Dirichlet forms are the major tools used to prove IU.
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On the nature and decay of quantum relative entropy
… generalizations of the strong subadditivity inequality and uncertainty-like entropy inequalities to subalgebras of operators on quantum systems for which usual independence assumptions fail. We construct new measures of non-classicality that simultaneously quantify entanglement and …
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Relaxation to equilibrium for kinetic Fokker-Planck equation
We want to study long-time behaviour of solutions $f_t$ of kinetic Fokker-Planck equation in $\mathbb{R}^d$, namely their convergence towards equilibrium $f_\infty$ in the form \[ \textrm{d}(f_t,f_\infty)\leq C_1 e^{-C_2 t}\textrm{d}(f_0,\mu) \] for appropriate distances $\textit{d}$ and constants …