Gaussian limit for Pfaffian point processes

2025/04/20 by Wang, Kai, Xu, Mei
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2504.14487

Abstract

We prove a central limit theorem for linear statistics of a broad class of Pfaffian point processes. As an application, we derive Gaussian limits for scaled linear statistics of step functions in the Pfaffian Sine₄ and Sine₁ processes.

Citations

• Widom's conjecture: variance asymptotics and entropy bounds for counting statistics of free fermions
• Pfaffian Point Processes from Free Fermion Algebras: Perfectness and Conditional Measures
• Conditional measures for Pfaffian point processes: conditioning on a bounded domain
• DLR equations and rigidity for the Sine-beta process
• CLT for fluctuations of linear statistics in the Sine-beta process
• Operator limit of the circular beta ensemble
• Correlation functions for zeros of a Gaussian power series and Pfaffians
• Eynard-Mehta theorem, Schur process, and their pfaffian analogs
• Correlation functions for symmetrized increasing subsequences
• Gaussian limit for determinantal random point fields
• Central Limit Theorem for local linear statistics in classical compact groups and related combinatorial identities
• On fluctuations of eigenvalues of random Hermitian matrices

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• A tail estimate for empirical processes of multivariate Gaussian under general dependence