• Corpus ID: 237571615

The Bessel Line Ensemble

@inproceedings{Wu2021TheBL,
  title={The Bessel Line Ensemble},
  author={Xuan Wu},
  year={2021}
}
  • Xuan Wu
  • Published 19 September 2021
  • Mathematics
. In this paper, we construct the Bessel line ensemble, a countable collection of continuous random curves. This line ensemble is stationary under horizontal shifts with the Bessel point process as its one-time marginal. Its finite dimensional distributions are given by the extended Bessel kernel. Furthermore, it enjoys a novel resampling invariance with respect to non-intersecting squared Bessel bridges. The Bessel line ensemble is constructed by extracting the hard edge scaling limit of a… 

Figures from this paper

References

SHOWING 1-10 OF 41 REFERENCES

Brownian regularity for the KPZ line ensemble

This paper seeks a quantitative comparison between the curves in the KPZ line ensemble [CH16] and a standard Brownian bridge under the $t^{1/3}$ vertical and $t^{2/3}$ horizontal scaling. The

Noncolliding Squared Bessel Processes

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

Brownian regularity for the Airy line ensemble, and multi-polymer watermelons in Brownian last passage percolation

  • A. Hammond
  • Mathematics
    Memoirs of the American Mathematical Society
  • 2022
The Airy line ensemble is a positive-integer indexed system of random continuous curves whose finite dimensional distributions are given by the multi-line Airy process. It is a natural object in the

Brownian Gibbs property for Airy line ensembles

Consider a collection of N Brownian bridges $B_{i}:[-N,N] \to \mathbb{R} $, Bi(−N)=Bi(N)=0, 1≤i≤N, conditioned not to intersect. The edge-scaling limit of this system is obtained by taking a weak

TIGHTNESS AND LOCAL FLUCTUATION ESTIMATES FOR THE KPZ LINE ENSEMBLE

Abstract. In this paper we study the KPZ line ensemble H = {Hn}n∈N under the t 1/3 vertical and t horizontal scaling. We prove quantitative (uniformly in t) local fluctuation estimates on curves in H

Brownian structure in the KPZ fixed point

Many models of one-dimensional local random growth are expected to lie in the Kardar-Parisi-Zhang (KPZ) universality class. For such a model, the interface profile at advanced time may be viewed in

Transversal Fluctuations of the ASEP, Stochastic Six Vertex Model, and Hall-Littlewood Gibbsian Line Ensembles

We consider the ASEP and the stochastic six vertex model started with step initial data. After a long time, T, it is known that the one-point height function fluctuations for these systems are of

EIGENVALUES OF THE LAGUERRE PROCESS AS NON-COLLIDING SQUARED BESSEL PROCESSES

Let A(t) be a np 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 as the Laguerre

Convergence of the KPZ Line Ensemble

  • Xuan Wu
  • Mathematics
    International Mathematics Research Notices
  • 2022
In this paper we study the Kardar–Parisi–Zhang (KPZ) line ensemble under the KPZ scaling. Based on their Gibbs property, we derive quantitative local fluctuation estimates for the scaled KPZ line