Deformed single ring theorems
Journal of Functional Analysis, ISSN: 0022-1236, Vol: 288, Issue: 5, Page: 110797
2025
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Example: if you select the 1-year option for an article published in 2019 and a metric category shows 90%, that means that the article or review is performing better than 90% of the other articles/reviews published in that journal in 2019. If you select the 3-year option for the same article published in 2019 and the metric category shows 90%, that means that the article or review is performing better than 90% of the other articles/reviews published in that journal in 2019, 2018 and 2017.
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Article Description
Given a sequence of deterministic matrices A=AN and a sequence of deterministic nonnegative matrices Σ=ΣN such that A→a and Σ→σ in ⁎-distribution for some operators a and σ in a finite von Neumann algebra A. Let U=UN and V=VN be independent Haar-distributed unitary matrices. We use free probability techniques to prove that, under mild assumptions, the empirical eigenvalue distribution of UΣV⁎+A converges to the Brown measure of T+a, where T∈A is an R -diagonal operator freely independent from a and |T| has the same distribution as σ. The assumptions can be removed if A is Hermitian or unitary. By putting A=0, our result removes a regularity assumption in the single ring theorem by Guionnet, Krishnapur and Zeitouni. We also prove a local convergence on optimal scale, extending the local single ring theorem of Bao, Erdős and Schnelli.
Bibliographic Details
http://www.sciencedirect.com/science/article/pii/S0022123624004853; http://dx.doi.org/10.1016/j.jfa.2024.110797; http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=85212071663&origin=inward; https://linkinghub.elsevier.com/retrieve/pii/S0022123624004853; https://dx.doi.org/10.1016/j.jfa.2024.110797
Elsevier BV
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