Brown's Spectral Distribution Measure for R-Diagonal Elements in Finite von Neumann Algebras☆

By Uffe Haagerup, F. Larsen. 2000

194 citations recorded by the source corpus.

Subfields: Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/437998c7d1b07342c1631930433a1503621840fe

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In Mathematical Physics

In Statistics and Probability

Citations in the corpus

Rectangular random matrices, related convolution (2005, background): “For example, it can be proved (combined results of [14,17]) that the asymptotic singular law of the sum of two independent random matrices whose distributions are invariant under left and right actions of the unitary group and whose singular laws converge weakly to probability measures μ1, μ2, only ”
Free Probability and Random Matrices (2014, methodology): “We give some key ideas of the proof from [85]; for another proof see [158].”
Eigenvalues of non-hermitian random matrices and Brown measure of non-normal operators: hermitian reduction and linearization method (2015, methodology): “[23] F. Larsen,Brown measures and R-diagonal elements in finite von Neumannalgebras, PhD thesis, University of Southern Denmark, 1999.”
Outlier Eigenvalues for Deformed I.I.D. Random Matrices (2014, background): “The probability measure β has a natural interpretation within the framework of operator algebra and free probability, see [50, 12, 32].”
Invariant subspaces for operators in a general II1-factor (2006, methodology): “The Brown measure of an operator T has been computed explicitly for a number of special operators (see [ HL ], [BL] and [DH2]).”
Spectrum of Markov Generators on Sparse Random Graphs (2012, background): “This phenomenon, not unusual for Brown measures, occurs for the circular law and more generally for R-diagonal operators, see Haagerup and Larsen [26].”
Around the circular law (2011, background): “This is connected to R-diagonal elements of free probability [75]; • If X11 has infinite fourth moment then the eigenvalues of largest modulus blow up and are asymptotically independent (Poisson statistics); • A large deviations principle for μX at speed n which includes as a special case the one ob”
Generating random density matrices (2010, result): “In [44], it is shown that the Brown measure of w̃ is a rotationally invariant measure, supported on the centered disk of radius √ k with radial density”
Lectures on the Combinatorics of Free Probability (2006, background): “[36] U. Haagerup and F. Larsen: Brown’s spectral distribution measure for Rdiagonal elements in finite von Neumann algebras, Journal of Functional Analysis 176 (2000), 331–367.”
Dynamical Isometry and a Mean Field Theory of RNNs: Gating Enables Signal Propagation in Recurrent Neural Networks (2018, background): “It turns out that as N → ∞ there is sufﬁcient self-averaging to overcome the dependencies induced by weight tying and the asymptotic singular value distributions of ˆ J and J are actually identical (Haagerup & Larsen, 2000).”
The single ring theorem (2009, methodology): “Let S denote the S-transform of Θ ♯2 (see [ 11, Section 2 ] for”