scholarly journals Cumulants for finite free convolution

2018 ◽  
Vol 155 ◽  
pp. 244-266
Author(s):  
Octavio Arizmendi ◽  
Daniel Perales
Keyword(s):  
Free Convolution

scholarly journals Representations of classical Lie groups and quantized free convolution

2015 ◽  
Vol 25 (3) ◽  
pp. 763-814 ◽  
Author(s):  
Alexey Bufetov ◽  
Vadim Gorin
Keyword(s):  
Lie Groups ◽  
Free Convolution

scholarly journals EMPIRICAL DISTRIBUTIONS OF LAPLACIAN MATRICES OF LARGE DILUTE RANDOM GRAPHS

2012 ◽  
Vol 01 (03) ◽  
pp. 1250004 ◽  
Author(s):  
TIEFENG JIANG
Keyword(s):  
Random Graph ◽  
Random Graphs ◽  
Spectral Properties ◽  
Empirical Distribution ◽  
Laplacian Matrix ◽  
Free Convolution ◽  
Laplacian Matrices ◽  
Empirical Distributions ◽  
Large N ◽  
Eigenvalues Of The Laplacian

We study the spectral properties of the Laplacian matrices and the normalized Laplacian matrices of the Erdös–Rényi random graph G(n, pn) for large n. Although the graph is simple, we discover some interesting behaviors of the two Laplacian matrices. In fact, under the dilute case, that is, pn ∈ (0, 1) and npn → ∞, we prove that the empirical distribution of the eigenvalues of the Laplacian matrix converges to a deterministic distribution, which is the free convolution of the semi-circle law and N(0, 1). However, for its normalized version, we prove that the empirical distribution converges to the semi-circle law.

scholarly journals Lévy-Hinčin type theorems for multiplicative and additive free convolution

1992 ◽  
Vol 153 (2) ◽  
pp. 217-248 ◽  
Author(s):  
Hari Bercovici ◽  
Dan-Virgil Voiculescu
Keyword(s):  
Free Convolution
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