Traffic Distributions and Independence: Permutation Invariant Random Matrices and the Three Notions of Independence

DOI10.1090/memo/1300zbMath1487.60002arXiv1111.4662OpenAlexW3120049962MaRDI QIDQ4983683

Camille Male

Publication date: 26 April 2021

Published in: Memoirs of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1111.4662

zbMATH Keywords

random matriceslimit theoremsfree probabilityoperads

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Random matrices (probabilistic aspects) (60B20) Free probability and free operator algebras (46L54) Random matrices (algebraic aspects) (15B52) Research exposition (monographs, survey articles) pertaining to probability theory (60-02) Operads (general) (18M60)

Related Items (13)

On the partial transpose of a Haar unitary matrix ⋮ Operads of (noncrossing) partitions, interacting bialgebras, and moment-cumulant relations ⋮ Hidden symmetries and large \(N\) factorisation for permutation invariant matrix observables ⋮ Fluctuation moments induced by conjugation with asymptotically liberating random matrix ensembles ⋮ Free component analysis: theory, algorithms and applications ⋮ Asymptotic freeness of unitary matrices in tensor product spaces for invariant states ⋮ Spectral asymptotics for contracted tensor ensembles ⋮ Traffic distributions and independence. II: Universal constructions for traffic spaces ⋮ An operadic approach to operator-valued free cumulants ⋮ Polynomial with cyclic monotone elements with applications to Random Matrices with discrete spectrum ⋮ Semicircular families of general covariance from Wigner matrices with permuted entries ⋮ Amalgamated free Lévy processes as limits of sample covariance matrices ⋮ Joint global fluctuations of complex Wigner and deterministic matrices

Cites Work

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• Freeness and the transposes of unitarily invariant random matrices
• The limiting distributions of large heavy Wigner and arbitrary random matrices
• A continuous semigroup of notions of independence between the classical and the free one
• Sharp bounds for sums associated to graphs of matrices
• Asymptotically free families of random unitaries in symmetric groups
• Integration with respect to the Haar measure on unitary, orthogonal and symplectic group
• Large random matrices: Lectures on macroscopic asymptotics. École d'Été des Probabilités de Saint-Flour XXXVI -- 2006
• Limit laws for random matrices and free products
• On certain free product factors via an extended matrix model
• On the limit distributions of random matrices with independent or free entries
• Combinatorics of free cumulants
• Rectangular random matrices, related convolution
• Semicircle law and freeness for random matrices with symmetries or correlations
• Lectures on the Combinatorics of Free Probability
• An Introduction to Random Matrices
• Some applications of freeness with amalgamation
• Asymptotic freeness by generalized moments for Gaussian and Wishart matrices. Application to beta random matrices

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