PlumX Metrics
Embed PlumX Metrics

Deformed single ring theorems

Journal of Functional Analysis, ISSN: 0022-1236, Vol: 288, Issue: 5, Page: 110797
2025
  • 0
    Citations
  • 0
    Usage
  • 0
    Captures
  • 0
    Mentions
  • 0
    Social Media
Metric Options:   Counts1 Year3 Year

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.

Provide Feedback

Have ideas for a new metric? Would you like to see something else here?Let us know