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math.OA2005★ 18 cited
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…
math.OA2003★ 4 cited
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…