2021/09/20 by Benigni, Lucas, Hung, Pei-Ken, Wu, Xuan
#FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.2109.09292
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 time-like or a space-like path, B is a determinantal point process with an explicit correlation kernel; for fixed t, \B(α,t),α∈ℕ0\ is an exponential Gibbsian line ensemble.