Remarks on free mutual information and orbital free entropy

DOI10.1215/00277630-3335530zbMath1348.46064arXiv1306.5372OpenAlexW3100235298MaRDI QIDQ2788613

Masaki Izumi, Yoshimichi Ueda

Publication date: 19 February 2016

Published in: Nagoya Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1306.5372

zbMATH Keywords

Loewner equationfree mutual informationorbital free entropyfree SDEliberation process

Mathematics Subject Classification ID

Free probability and free operator algebras (46L54) Measures of information, entropy (94A17)

Related Items (11)

Spectral distribution of the free Jacobi process, revisited ⋮ Functional equations solving initial-value problems of complex Burgers-type equations for one-dimensional log-gases ⋮ Inverse of the flow and moments of the free Jacobi process associated with one projection ⋮ Summing free unitary Brownian motions with applications to quantum information ⋮ On the free convolution with a free multiplicative analogue of the normal distribution ⋮ LIBERATION, FREE MUTUAL INFORMATION AND ORBITAL FREE ENTROPY ⋮ The spectral edge of unitary Brownian motion ⋮ Orbital free pressure and its Legendre transform ⋮ Schur–Weyl duality and the product of randomly-rotated symmetries by a unitary Brownian motion ⋮ Relating moments of self-adjoint polynomials in two orthogonal projections ⋮ Free Jacobi process associated with one projection: local inverse of the flow

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A free stochastic partial differential equation
• On free stochastic differential equations
• Segal-Bargmann transform, functional calculus on matrix spaces and the theory of semi-circular and circular systems
• On the free convolution with a free multiplicative analogue of the normal distribution
• Notes on microstate free entropy of projections
• Stochastic calculus with respect to free Brownian motion and analysis on Wigner space
• Processes with free increments
• The analogues of entropy and of Fisher's information measure in free probability theory. VI: Liberation and mutual free information
• Concavification of free entropy
• On some sublattices of the Leech lattice
• Liberation of projections
• Free Jacobi process
• Spectral distribution of the free Jacobi process
• FREE ENTROPY
• ORBITAL APPROACH TO MICROSTATE FREE ENTROPY
• Orbital free entropy, revisited

This page was built for publication: Remarks on free mutual information and orbital free entropy