Randomly incomplete spectra and intermediate statistics
O. Bohigas, M. P. Pato
TL;DR
This paper introduces a model for spectra with randomly missing levels, bridging the gap between complete spectra and Poisson spectra, and extends the Fredholm determinant formalism to incomplete random matrix theory spectra.
Contribution
It presents a novel formalism for describing incomplete spectra and demonstrates its application to RMT and picket fence spectra, extending existing mathematical tools.
Findings
The model effectively describes the transition from complete to Poisson spectra.
The Fredholm determinant formalism is extended to incomplete spectra.
The approach applies to both RMT and deterministic spectra like picket fences.
Abstract
By randomly removing a fraction of levels from a given spectrum a model is constructed that describes a crossover from this spectrum to a Poisson spectrum. The formalism is applied to the transitions towards Poisson from random matrix theory (RMT) spectra and picket fence spectra. It is shown that the Fredholm determinant formalism of RMT extends naturally to describe incomplete RMT spectra.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.