Many–Body Aspects of Approach to Equilibrium
Many-body aspects of approach to equilibrium
Kinetic theory and approach to equilibrium is usually studied in the realm of the Boltzmann equation. With a few notable exceptions not much is known about the solutions of this equation and about its derivation from fundamental principles. In 1956 Mark Kac introduced a probabilistic model of interacting particles. The velocity distribution is governed by a Markov semi group and the evolution of its single particle marginals is governed (in the infinite particle limit) by a caricature of the spatially...
An application of the Bakry-Émery criterion to infinite dimensional diffusions
Short proofs of theorems of Mirsky and Horn on diagonals and eigenvalues of matrices.
Brascamp--Lieb inequalities for non-commutative integration.
Asymmetric covariance estimates of Brascamp–Lieb type and related inequalities for log-concave measures
An inequality of Brascamp and Lieb provides a bound on the covariance of two functions with respect to log-concave measures. The bound estimates the covariance by the product of the norms of the gradients of the functions, where the magnitude of the gradient is computed using an inner product given by the inverse Hessian matrix of the potential of the log-concave measure. Menz and Otto [Uniform logarithmic Sobolev inequalities for conservative spin systems with super-quadratic single-site potential....
Strong convergence towards homogeneous cooling states for dissipative Maxwell models
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