scholarly journals Limit theorems and soft edge of freezing random matrix models via dual orthogonal polynomials

2021 ◽  
Vol 62 (8) ◽  
pp. 083303
Author(s):  
Sergio Andraus ◽  
Kilian Hermann ◽  
Michael Voit
Keyword(s):  
Orthogonal Polynomials ◽  
Matrix Models ◽  
Random Matrix ◽  
Limit Theorems ◽  
Random Matrix Models ◽  
Soft Edge

Universality in invariant random-matrix models: Existence near the soft edge

1997 ◽  
Vol 55 (3) ◽  
pp. 3712-3715 ◽  
Author(s):  
E. Kanzieper ◽  
V. Freilikher
Keyword(s):  
Matrix Models ◽  
Random Matrix ◽  
Random Matrix Models ◽  
Soft Edge

scholarly journals Hidden noise structure and random matrix models of stock correlations

2012 ◽  
Vol 12 (4) ◽  
pp. 567-572 ◽  
Author(s):  
Ivailo I. Dimov ◽  
Petter N. Kolm ◽  
Lee Maclin ◽  
Dan Y. C. Shiber
Keyword(s):  
Matrix Models ◽  
Random Matrix ◽  
Noise Structure ◽  
Random Matrix Models

scholarly journals Random matrix models for phase diagrams

2011 ◽  
Vol 74 (10) ◽  
pp. 102001 ◽  
Author(s):  
B Vanderheyden ◽  
A D Jackson
Keyword(s):  
Matrix Models ◽  
Phase Diagrams ◽  
Random Matrix ◽  
Random Matrix Models

scholarly journals Non-Hermitian random matrix models: Free random variable approach

1997 ◽  
Vol 55 (4) ◽  
pp. 4100-4106 ◽  
Author(s):  
Romuald A. Janik ◽  
Maciej A. Nowak ◽  
Gábor Papp ◽  
Jochen Wambach ◽  
Ismail Zahed
Keyword(s):  
Matrix Models ◽  
Random Matrix ◽  
Random Variable ◽  
Variable Approach ◽  
Random Matrix Models

scholarly journals FREE DETERMINISTIC EQUIVALENTS, RECTANGULAR RANDOM MATRIX MODELS, AND OPERATOR-VALUED FREE PROBABILITY THEORY

2012 ◽  
Vol 01 (02) ◽  
pp. 1150008 ◽  
Author(s):  
ROLAND SPEICHER ◽  
CARLOS VARGAS
Keyword(s):  
Matrix Models ◽  
Random Matrix ◽  
Collective Behavior ◽  
Free Probability ◽  
Matrix Problem ◽  
Free Probability Theory ◽  
Random Matrix Model ◽  
Deterministic Equivalent ◽  
Cauchy Transforms ◽  
Random Matrix Models

Motivated by the asymptotic collective behavior of random and deterministic matrices, we propose an approximation (called "free deterministic equivalent") to quite general random matrix models, by replacing the matrices with operators satisfying certain freeness relations. We comment on the relation between our free deterministic equivalent and deterministic equivalents considered in the engineering literature. We do not only consider the case of square matrices, but also show how rectangular matrices can be treated. Furthermore, we emphasize how operator-valued free probability techniques can be used to solve our free deterministic equivalents. As an illustration of our methods we show how the free deterministic equivalent of a random matrix model from [6] can be treated and we thus recover in a conceptual way the results from [6]. On a technical level, we generalize a result from scalar-valued free probability, by showing that randomly rotated deterministic matrices of different sizes are asymptotically free from deterministic rectangular matrices, with amalgamation over a certain algebra of projections. In Appendix A, we show how estimates for differences between Cauchy transforms can be extended from a neighborhood of infinity to a region close to the real axis. This is of some relevance if one wants to compare the original random matrix problem with its free deterministic equivalent.

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