Gap probability for products of random matrices in the critical regime
نویسندگان
چکیده
The singular values of a product M independent Ginibre matrices size N×N form determinantal point process. Near the soft edge, as both and N go to infinity in such way that M/N→α, α>0, scaling limit emerges. We consider gap probability for corresponding limiting process, namely, there are no particles interval (a,+∞). derive Tracy–Widom-like formula terms unique solution certain matrix Riemann–Hilbert problem 2 × 2. right-tail asymptotics this is obtained by Deift–Zhou non-linear steepest descent analysis.
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 2022
ISSN: ['0021-9045', '1096-0430']
DOI: https://doi.org/10.1016/j.jat.2021.105687