Brown measure of \(R\)-diagonal operators, revisited

DOI10.1007/978-3-031-38020-4_10MaRDI QIDQ6620635

Ping Zhong

Publication date: 17 October 2024

Mathematics Subject Classification ID

Selfadjoint operator algebras ((C^*)-algebras, von Neumann ((W^*)-) algebras, etc.) (46Lxx) Special classes of linear operators (47Bxx) General theory of linear operators (47Axx) Integral, integro-differential, and pseudodifferential operators (47Gxx)

Cites Work

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• Around the circular law
• Free probability and random matrices
• The single ring theorem
• Decompositions of the free additive convolution
• A decomposition theorem in \(\mathrm{II}_{1}\)-factors
• The Lebesgue decomposition of the free additive convolution of two probability distributions
• Invariant subspaces for operators in a general \(\text{II}_{1}\)-factor
• Limit laws for random matrices and free products
• Brown's spectral distribution measure for \(R\)-diagonal elements in finite von Neumann algebras
• Eigenvalues of non-Hermitian random matrices and Brown measure of non-normal operators: Hermitian reduction and linearization method
• An upper triangular decomposition theorem for some unbounded operators affiliated to \(\mathrm{II}_{1}\)-factors
• Commutators of free random variables
• Local single ring theorem on optimal scale
• A new approach to subordination results in free probability
• Determinant theory in finite factors
• \(R\)-diagonal elements and freeness with amalgamation
• Resolvents of $\mathscr{R}$-diagonal operators
• Brown measures of unbounded operators affiliated with a finite von Neumann algebra
• $R$-diagonal pairs - a common approach to Haar unitaries and circular elements
• The Law of Large Numbers for the Free Multiplicative Convolution

Related Items (1)

Deformed single ring theorems

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