Universality of the Stochastic Bessel Operator

@article{Rider2016UniversalityOT,
  title={Universality of the Stochastic Bessel Operator},
  author={B. Rider and Patrick Waters},
  journal={Probability Theory and Related Fields},
  year={2016},
  pages={1-44}
}
We establish universality at the hard edge for general beta ensembles assuming that: the background potential V is a polynomial such that $$x \mapsto V(x^2)$$x↦V(x2) is strongly convex, $$\beta \ge 1$$β≥1, and the “dimension-difference” parameter $$a\ge 0$$a≥0. The method rests on the corresponding tridiagonal matrix models, showing that their appropriate continuum scaling limit is given by the Stochastic Bessel Operator. As conjectured in Edelman and Sutton (J Stat Phys 127:1121–1165, 2007… Expand
4 Citations
Feynman-Kac formula for the stochastic Bessel operator
  • PDF
The random matrix hard edge: rare events and a transition
  • 1
  • PDF
On a distinguished family of random variables and Painlev\'e equations
  • 1
  • PDF

References

SHOWING 1-10 OF 24 REFERENCES
Beta ensembles, stochastic Airy spectrum, and a diffusion
  • 201
  • PDF
Spiking the random matrix hard edge
  • 4
  • PDF
Edge Universality of Beta Ensembles
  • 119
  • PDF
Level spacing distributions and the Bessel kernel
  • 267
  • PDF
Transport Maps for $${\beta}$$β-Matrix Models and Universality
  • 48
  • Highly Influential
  • PDF
Diffusion at the Random Matrix Hard Edge
  • 55
  • PDF
Universality for Eigenvalue Correlations at the Origin of the Spectrum
  • 67
  • PDF
Universality of the Stochastic Airy Operator
  • 54
  • PDF
Universality for Orthogonal and Symplectic Laguerre-Type Ensembles
  • 29
  • PDF
Universality at the edge of the spectrum for unitary, orthogonal, and symplectic ensembles of random matrices
  • 126
  • PDF
...
1
2
3
...