scholarly journals Convergence of the eigenvalue density for Laguerre beta ensembles on short scales

2014 ◽  
Vol 19 (0) ◽  
Author(s):  
Philippe Sosoe ◽  
Percy Wong
Keyword(s):  
Eigenvalue Density ◽  
Beta Ensembles

scholarly journals The bead process for beta ensembles

2021 ◽  
Author(s):  
Joseph Najnudel ◽  
Bálint Virág
Keyword(s):  
Point Processes ◽  
Scaling Limit ◽  
Companion Paper ◽  
Point Counting ◽  
Infinite Dimensional ◽  
Transition Mechanism ◽  
Beta Ensemble ◽  
Beta Ensembles ◽  
Orthogonal Ensembles ◽  
Gaussian Beta Ensembles

AbstractThe bead process introduced by Boutillier is a countable interlacing of the $${\text {Sine}}_2$$ Sine 2 point processes. We construct the bead process for general $${\text {Sine}}_{\beta }$$ Sine β processes as an infinite dimensional Markov chain whose transition mechanism is explicitly described. We show that this process is the microscopic scaling limit in the bulk of the Hermite $$\beta $$ β corner process introduced by Gorin and Shkolnikov, generalizing the process of the minors of the Gaussian Unitary and Orthogonal Ensembles. In order to prove our results, we use bounds on the variance of the point counting of the circular and the Gaussian beta ensembles, proven in a companion paper (Najnudel and Virág in Some estimates on the point counting of the Circular and the Gaussian Beta Ensemble, 2019).

scholarly journals Moments of traces of circular beta-ensembles

2015 ◽  
Vol 43 (6) ◽  
pp. 3279-3336 ◽  
Author(s):  
Tiefeng Jiang ◽  
Sho Matsumoto
Keyword(s):  
Beta Ensembles

scholarly journals Matrix models for beta ensembles

2002 ◽  
Vol 43 (11) ◽  
pp. 5830-5847 ◽  
Author(s):  
Ioana Dumitriu ◽  
Alan Edelman
Keyword(s):  
Matrix Models ◽  
Beta Ensembles

scholarly journals Universality of general $\beta$ -ensembles

2014 ◽  
Vol 163 (6) ◽  
pp. 1127-1190 ◽  
Author(s):  
Paul Bourgade ◽  
László Erdős ◽  
Horng-Tzer Yau
Keyword(s):  
Beta Ensembles

scholarly journals Eigenvalue density of the doubly correlated Wishart model: exact results

2015 ◽  
Vol 48 (17) ◽  
pp. 175204 ◽  
Author(s):  
Daniel Waltner ◽  
Tim Wirtz ◽  
Thomas Guhr
Keyword(s):  
Exact Results ◽  
Eigenvalue Density

scholarly journals On Certain Translation Invariant Properties of Interior Transmission Spectra and Their Doppler’s Effect

2017 ◽  
Vol 2017 ◽  
pp. 1-9
Author(s):  
Lung-Hui Chen
Keyword(s):  
Density Function ◽  
Functional Derivative ◽  
Index Of Refraction ◽  
Velocity Variation ◽  
Transmission Spectra ◽  
Motion Velocity ◽  
Translation Invariant ◽  
Eigenvalue Density ◽  
Position Variable ◽  
Invariant Properties

We study the translation invariant properties of the eigenvalues of scattering transmission problem. We examine the functional derivative of the eigenvalue density function Δ(x^) to the defining index of refraction n(x). By the limit behaviors in frequency sphere, we prove some results on the inverse uniqueness of index of refraction. In physics, Doppler’s effect connects the variation of the frequency/eigenvalue and the motion velocity/variation of position variable. In this paper, we proved the functional derivative ∂rΔx^=(1+nrx^)/π.

scholarly journals Edge Universality of Beta Ensembles

2014 ◽  
Vol 332 (1) ◽  
pp. 261-353 ◽  
Author(s):  
Paul Bourgade ◽  
László Erdös ◽  
Horng-Tzer Yau
Keyword(s):  
Beta Ensembles

scholarly journals Gap universality of generalized Wigner and $\beta$-ensembles

2015 ◽  
Vol 17 (8) ◽  
pp. 1927-2036 ◽  
Author(s):  
László Erdős ◽  
Horng-Tzer Yau
Keyword(s):  
Beta Ensembles

Diffusion onGL(N,C)/U(N)and Eigenvalue Density forN→∞Limit

1998 ◽  
Vol 67 (2) ◽  
pp. 421-425
Author(s):  
Toshinao Akuzawa ◽  
Miki Wadati
Keyword(s):  
Eigenvalue Density
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