Central limit theorem for the determinantal point process with the confluent hypergeometric kernel

2025/05/21 by Sergei M. Gorbunov, Gorbunov, Sergei M.
Mathematics · Computer Science · #Random Matrices and Applications #Point processes and geometric inequalities #Bayesian Methods and Mixture Models

paper · pdf · doi:10.48550/arxiv.2505.16069

Abstract

We consider the convergence of additive functionals under the determinantal point process with the confluent hypergeometric kernel, corresponding to a sufficiently smooth function f(x/R), as R→∞. We show that these functionals approach Gaussian distribution and give an estimate on the Kolmogorov-Smirnov distance. To obtain these results, we derive an exact identity for expectations of multiplicative functionals in terms of Fredholm determinants.

Citations

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Related

• Asymptotics of the deformed Fredholm determinant of the confluent hypergeometric kernel
• On the Fredholm determinant of the confluent hypergeometric kernel with discontinuities
• Asymptotics of the confluent hypergeometric process with a varying external potential in the super-exponential region
• Confluent hypergeometric kernel determinant on multiple large intervals
• Determinantal point processes associated with Bergman kernels: construction and limit theorems