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Operator level hard-to-soft transition for β -ensembles

Dumaz, Laure; Li, Yun; Valkó, Benedek (2021), Operator level hard-to-soft transition for β -ensembles, Electronic Journal of Probability, 26, p. 1-28. 10.1214/21-EJP602

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Type
Article accepté pour publication ou publié
Date
2021
Journal name
Electronic Journal of Probability
Volume
26
Publisher
Institute of Mathematical Statistics
Pages
1-28
Publication identifier
Metadata
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Author(s)
Dumaz, Laure
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Li, Yun
University of Wisconsin, Department of Mathematics
Valkó, Benedek
University of Wisconsin, Department of Mathematics
Abstract (EN)
The soft and hard edge scaling limits of β-ensembles can be characterized as the spectra of certain random Sturm-Liouville operators. It has been shown that by tuning the parameter of the hard edge process one can obtain the soft edge process as a scaling limit. We prove that this limit can be realized on the level of the corresponding random operators. More precisely, the random operators can be coupled in a way so that the scaled versions of the hard edge operators converge to the soft edge operator a.s. in the norm resolvent sense.
Subjects / Keywords
random differential operators; random matrices