scholarly journals The mean spectral measures of random Jacobi matrices related to Gaussian beta ensembles

2015 ◽  
Vol 20 (0) ◽  
Author(s):  
Khanh Trinh Duy ◽  
Tomoyuki Shirai
Keyword(s):  
Jacobi Matrices ◽  
Spectral Measures ◽  
The Mean ◽  
Random Jacobi Matrices ◽  
Beta Ensembles ◽  
Gaussian 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 Upper Bounds On Wavepacket Spreading For Random Jacobi Matrices

2007 ◽  
Vol 273 (3) ◽  
pp. 601-618 ◽  
Author(s):  
Svetlana Jitomirskaya ◽  
Hermann Schulz-Baldes
Keyword(s):  
Upper Bounds ◽  
Jacobi Matrices ◽  
Random Jacobi Matrices

Singular-unbounded random Jacobi matrices

2019 ◽  
Vol 60 (8) ◽  
pp. 081904
Author(s):  
Nishant Rangamani
Keyword(s):  
Jacobi Matrices ◽  
Random Jacobi Matrices
Sign in / Sign up

Export Citation Format

Share Document