24 August 2023
Proves CLTs for linear statistics of constrained Mittag-Leffler ensemble
Statistics based on bounded measurable functions converge to Gaussian process
Radius-dependent statistics also converge, as continuous-time processes
Particles' radial behavior approximated by independent random variables
Limit theorems for constrained Mittag-Leffler ensemble
This paper proves central limit theorems for linear statistics of the constrained Mittag-Leffler ensemble, a determinantal point process with radial symmetry. As the number of particles grows, fluctuations of rotationally-invariant statistics are shown to converge to Gaussian processes. Both statistics based on bounded measurable test functions, and radius-dependent statistics are covered. The proofs rely on approximating the particles' radial behavior with independent random variables.
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