5 citations · 6 across the 4 of their papers we have counts for
5 papers
An Inequality of Hadamard Type for Permanents
Eric Carlen, Elliott H. Lieb, Michael Loss
Let F be an N x N complex matrix whose jth column is the vector f_j in C^N. Let |f_j|^2 denote the sum of the absolute squares of the entries of f_j. Hadamard's inequality for dete…
A Sharp analog of Young's Inequality on and Related Entropy Inequalities
Eric Carlen, Elliott Lieb, Michael Loss
We prove a sharp analog of Young's inequality on , and deduce from it certain sharp entropy inequalities. The proof turns on constructing a nonlinear heat flow that drives tri…
Some Matrix Rearrangement Inequalities
Eric Carlen, Elliott H. Lieb
We investigate a rearrangement inequality for pairs of n-square matrices: Let |A\|_p denote the C^p trace norm of an n-square matrix A. Consider the quantity |A+B|_p^p + |A-B|_p^p.…
Constrained deepest descent in the 2-Wasserstein metric
E. A. Carlen, W. Gangbo
We study several constrained variational problem in the 2-Wasserstein metric for which the set of probability densities satisfying the constraint is not closed. For example, given…
Determination of the Spectral Gap for Kac's Master Equation and Related Stochastic Evolutions
Eric A. Carlen, Maria C. Carvalho, Michael Loss
We present a method for bounding, and in some cases computing, the spectral gap for systems of many particles evolving under the influence of a random collision mechanism. In parti…