3 papers
math.OA2026
The spectra of polynomials in free (semi)circular operators
Akihiro Miyagawa
We show that any -bounded rational function in free semicircular random variables is a bounded operator, which implies the coincidence of the usual spectrum and -spectrum…
math.PR2025
Double -Wigner Chaos and the Fourth Moment
Todd Kemp, Akihiro Miyagawa
In this paper, we prove the Fourth Moment Theorem for sequences of (noncommutative) random variables given as sums of two stochastic integrals in two different parity orders of cha…
math.OA2025
The strong Haagerup inequality for q-circular systems
Todd Kemp, Akihiro Miyagawa
Together with Speicher, in 2007 the first author proved the strong Haagerup inequality for operator norms of homogeneous holomorphic polynomials in freely independent …