scholarly journals The Largest Eigenvalue of Real Symmetric, Hermitian and Hermitian Self-dual Random Matrix Models with Rank One External Source, Part I

2012 ◽  
Vol 146 (4) ◽  
pp. 719-761 ◽  
Author(s):  
Dong Wang
Keyword(s):  
Matrix Models ◽  
Random Matrix ◽  
External Source ◽  
Largest Eigenvalue ◽  
Rank One ◽  
Random Matrix Models ◽  
The Largest Eigenvalue

scholarly journals Emergent fractal phase in energy stratified random models

2021 ◽  
Vol 11 (6) ◽  
Author(s):  
Anton Kutlin ◽  
Ivan Khaymovich
Keyword(s):  
Brownian Motion ◽  
Matrix Models ◽  
Random Matrix ◽  
Stochastic Matrix ◽  
Spectral Structure ◽  
Translation Invariant ◽  
Random Models ◽  
Rank One ◽  
Partial Correlations ◽  
Random Matrix Models

We study the effects of partial correlations in kinetic hopping terms of long-range disordered random matrix models on their localization properties. We consider a set of models interpolating between fully-localized Richardson’s model and the celebrated Rosenzweig-Porter model (with implemented translation-invariant symmetry). In order to do this, we propose the energy-stratified spectral structure of the hopping term allowing one to decrease the range of correlations gradually. We show both analytically and numerically that any deviation from the completely correlated case leads to the emergent non-ergodic delocalization in the system unlike the predictions of localization of cooperative shielding. In order to describe the models with correlated kinetic terms, we develop the generalization of the Dyson Brownian motion and cavity approaches basing on stochastic matrix process with independent rank-one matrix increments and examine its applicability to the above set of models.

Large N-limit for random matrices with external source with three distinct eigenvalues

2016 ◽  
Vol 05 (02) ◽  
pp. 1650005
Author(s):  
Jian Xu ◽  
Engui Fan ◽  
Yang Chen
Keyword(s):  
Matrix Models ◽  
Random Matrices ◽  
Random Matrix ◽  
Hilbert Problem ◽  
External Source ◽  
Universal Behavior ◽  
Large N ◽  
Random Matrix Models ◽  
Riemann Hilbert Problem ◽  
Sine Kernel

In this paper, we analyze the large N-limit for random matrix with external source with three distinct eigenvalues. And we confine ourselves in the Hermite case and the three distinct eigenvalues are [Formula: see text]. For the case [Formula: see text], we establish the universal behavior of local eigenvalue correlations in the limit [Formula: see text], which is known from unitarily invariant random matrix models. Thus, local eigenvalue correlations are expressed in terms of the sine kernel in the bulk and in terms of the Airy kernel at the edge of the spectrum. The result can be obtained by analyzing [Formula: see text] Riemann–Hilbert problem via nonlinear steepest decent method.

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
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