Edge Distribution of Thinned Real Eigenvalues in the Real Ginibre Ensemble

@article{Baik2022EdgeDO,
  title={Edge Distribution of Thinned Real Eigenvalues in the Real Ginibre Ensemble},
  author={Jinho Baik and Thomas Bothner},
  journal={Annales Henri Poincar{\'e}},
  year={2022}
}
This paper is concerned with the explicit computation of the limiting distribution function of the largest real eigenvalue in the real Ginibre ensemble when each real eigenvalue has been removed independently with constant likelihood. We show that the recently discovered integrable structures in [2] generalize from the real Ginibre ensemble to its thinned equivalent. Concretely, we express the aforementioned limiting distribution function as a convex combination of two simple Fredholm… 
Asymptotic expansions for a class of Fredholm Pfaffians and interacting particle systems
Motivated by the phenomenon of duality for interacting particle systems we introduce two classes of Pfaffian kernels describing a number of Pfaffian point processes in the ‘bulk’ and at the ‘edge’.

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