# Determinantal structures for Bessel fields

@inproceedings{Benigni2021DeterminantalSF, title={Determinantal structures for Bessel fields}, author={Lucas Benigni and Pei-Ken Hung and Xuan Wu}, year={2021} }

A Bessel field B = {B(α, t), α ∈ N0, t ∈ R} is a two-variable random field such that for every (α, t), B(α, t) has the law of a Bessel point process with index α. The Bessel fields arise as hard edge scaling limits of the Laguerre field, a natural extension of the classical Laguerre unitary ensemble. It is recently proved in [LW21] that for fixed α, {B(α, t), t ∈ R} is a squared Bessel Gibbsian line ensemble. In this paper, we discover rich integrable structures for the Bessel fields: along a…

#### References

SHOWING 1-10 OF 45 REFERENCES

Eigenvalues of the Laguerre Process as Non-Colliding Squared Bessel Processes

- Mathematics
- 2001

Let $A(t)$ be an $n\times p$ matrix with independent standard complex Brownian entries and set $M(t)=A(t)^*A(t)$. This is a process version of the Laguerre ensemble and as such we shall refer to it…

Noncolliding Squared Bessel Processes

- Mathematics, Physics
- 2011

We consider a particle system of the squared Bessel processes with index ν>−1 conditioned never to collide with each other, in which if −1<ν<0 the origin is assumed to be reflecting. When the number…

Optimal soft edge scaling variables for the Gaussian and Laguerre even β ensembles

- Mathematics, PhysicsNuclear Physics B
- 2019

Abstract The β ensembles are a class of eigenvalue probability densities which generalise the invariant ensembles of classical random matrix theory. In the case of the Gaussian and Laguerre weights,…

Level spacing distributions and the Bessel kernel

- Mathematics, Physics
- 1994

AbstractScaling models of randomN×N hermitian matrices and passing to the limitN→∞ leads to integral operators whose Fredholm determinants describe the statistics of the spacing of the eigenvalues of…

Markov property of determinantal processes with extended sine, Airy, and Bessel kernels

- Mathematics, Physics
- 2011

When the number of particles is finite, the noncolliding Brownian motion (the Dyson model) and the noncolliding squared Bessel process are determinantal diffusion processes for any deterministic…

Determinantal random point fields

- Mathematics, Physics
- 2000

This paper contains an exposition of both recent and rather old results on determinantal random point fields. We begin with some general theorems including proofs of necessary and sufficient…

On the Partial Connection Between Random Matrices and Interacting Particle Systems

- Mathematics, Physics
- 2010

In the last decade there has been increasing interest in the fields of random matrices, interacting particle systems, stochastic growth models, and the connections between these areas. For instance,…

Asymptotics of Plancherel measures for symmetric groups

- Mathematics
- 1999

1.1. Plancherel measures. Given a finite group G, by the corresponding Plancherel measure we mean the probability measure on the set G∧ of irreducible representations of G which assigns to a…

The Laguerre Unitary Process

- Mathematics, Physics
- 2019

We define a new matrix-valued stochastic process with independent stationary increments from the Laguerre Unitary Ensemble, which in a certain sense may be considered a matrix generalisation of the…

A Brownian‐Motion Model for the Eigenvalues of a Random Matrix

- Mathematics
- 1962

A new type of Coulomb gas is defined, consisting of n point charges executing Brownian motions under the influence of their mutual electrostatic repulsions. It is proved that this gas gives an exact…