2021/09/19 by Xuan Wu, Wu, Xuan
Computer Science · Economics, Econometrics and Finance · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2109.09070
openalex publication_date 2021/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 collection of independent squared Bessel processes starting at the origin and never being conditioned to intersect. This process is also known as the Dyson Bessel process, and it arises as the evolution of the eigenvalues of the Laguerre unitary ensemble with i.i.d. complex Brownian entries.