Fetching the paper…

Reading the bibliography…

2025

Computing extreme singular values of free operators

Parmaksiz, Emre, van Handel, Ramon

Original
PDF
Post on X

Understand

A recent development in random matrix theory, the intrinsic freeness principle, establishes that the spectrum of very general random matrices behaves as that of an associated free operator.

This reduces the study of such random matrices to the deterministic problem of computing spectral statistics of the free operator.
In the self-adjoint case, the spectral edges of the free operator can be computed exactly by means of a variational formula due to Lehner.
In this note, we provide variational formulas for the largest and smallest singular values in the non-self-adjoint case.

Computing extreme singular values of free operators · Around

Built on

Computing norms of free operators with matrix coefficients
F. Lehner · 1999
Earlier work this paper cites.
A new application of random matrices: Ext ⁡ ( C red ∗ ( F 2 ) ) {\rm Ext}(C^{*}_{\rm red}(F_{2})) is not a group
U. Haagerup and S. Thorbjørnsen · 2005
Earlier work this paper cites.
The Schur complement and its applications
F. Zhang, editor · 2005
Earlier work this paper cites.

Similar

Lectures on the combinatorics of free probability
A. Nica and R. Speicher · 2006
Cited alongside, same era.
Matrix concentration inequalities and free probability
A. S. Bandeira, M. T. Boedihardjo, and R. van Handel · 2023
Cited alongside, same era.
Matrix concentration inequalities and free probability II. Two-sided bounds and applications, 2024
Original
A. S. Bandeira, G. Cipolloni, D. Schröder, and R. van Handel · 2024
Cited alongside, same era.

Then

Universality and sharp matrix concentration inequalities
T. Brailovskaya and R. van Handel · 2024
Later among the works it cites.
The strong convergence phenomenon
Original
R. van Handel · 2026
Closest in time.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…