Operator level hard-to-soft transition for $\beta$-ensembles

Laure Dumaz; Yun Li; Benedek Valkó

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arXiv · 2003.02779

Operator level hard-to-soft transition for $\beta$-ensembles

Laure Dumaz·Yun Li·Benedek Valkó

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Abstract

The soft and hard edge scaling limits of $\beta$-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.

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BibTeX RIS

Laure Dumaz, Yun Li, Benedek Valkó. 2020-03-05. Operator level hard-to-soft transition for $\beta$-ensembles. https://arxiv.org/abs/2003.02779

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