scholarly journals Fast sampling from $$\beta $$-ensembles

2021 ◽  
Vol 31 (1) ◽  
Author(s):  
Guillaume Gautier ◽  
Rémi Bardenet ◽  
Michal Valko
Keyword(s):  
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 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

scholarly journals Limits for circular Jacobi beta-ensembles

2017 ◽  
Vol 215 ◽  
pp. 40-67 ◽  
Author(s):  
Dang-Zheng Liu
Keyword(s):  
Beta Ensembles
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