18 citations · 32 across the 6 of their papers we have counts for
7 papers
Large deviations for functions of two random projection matrices
F. Hiai, D. Petz
In this paper two independent and unitarily invariant projection matrices P(N) and Q(N) are considered and the large deviation is proven for the eigenvalue density of all polynomia…
A free analogue of the transportation cost inequality on the circle
F. Hiai, D. Petz
We give a new proof of the free transportation cost inequality for measures on the circle following M. Ledoux's idea.
Large deviation for the empirical eigenvalue density of truncated Haar unitary matrices
Denes Petz, Julia Reffy
Let be an Haar unitary matrix and be its truncation. In this paper the large deviation is proven for the empirical eigenvalue density of…
A simple proof of the strong subadditivity inequality
Michael A. Nielsen, Denes Petz
Arguably the deepest fact known about the von Neumann entropy, the strong subadditivity inequality is a potent hammer in the quantum information theorist's toolkit. This short tuto…
Inequalities related to free entropy derived from random matrix approximation
Fumio Hiai, Denes Petz, Yoshimichi Ueda
Biane proved the free analog of the logarithmic Sobolev inequality for probability measures on the real line by means of random matrix approximation procedure. We show that the sam…
On asymptotics of large Haar distributed unitary matrices
Denes Petz, Julia Reffy
Let be an Haar unitary matrix. In this paper, the asymptotic normality and independence of $\Tr U_n, \Tr U_n^2, ..., \Tr U_n^k$ are shown by using elementary met…