Short proofs of theorems of Mirsky and Horn on diagonals and eigenvalues of matrices.
Brascamp--Lieb inequalities for non-commutative integration.
Convex Trace Functions and the Wigner-Yanase-Dyson Conjecture
On the lowest eigenvalue of the Laplacian for the intersection of two domains.
A Fundamental Property of Quantum-Mechanical Entropy
Proof of the Strong Subadditivity of Quantum-Mechanical Entropy
Symmetry of the Ginzburg-Landau minimizer in a disc
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....
Strichartz inequality for orthonormal functions
We prove a Strichartz inequality for a system of orthonormal functions, with an optimal behavior of the constant in the limit of a large number of functions. The estimate generalizes the usual Strichartz inequality, in the same fashion as the Lieb-Thirring inequality generalizes the Sobolev inequality. As an application, we consider the Schrödinger equation in a time-dependent potential and we show the existence of the wave operator in Schatten spaces.
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