File(s) not publicly available
The spectral edge of unitary Brownian motion
journal contribution
posted on 2023-06-09, 17:13 authored by Benoît Collins, Antoine DahlqvistAntoine Dahlqvist, Todd KempThe Brownian motion $$(UN_t)_{t\backslashge 0}$$(UtN)t=0on the unitary group converges, as a process, to the free unitary Brownian motion $$(u_t)_{t\backslashge 0}$$(ut)t=0as $$N\backslashrightarrow \backslashinfty $$N?8. In this paper, we prove that it converges strongly as a process: not only in distribution but also in operator norm. In particular, for a fixed time $$t>0$$t>0, we prove that the unitary Brownian motion has a spectral edge: there are no outlier eigenvalues in the limit. We also prove an extension theorem: any strongly convergent collection of random matrix ensembles independent from a unitary Brownian motion also converge strongly jointly with the Brownian motion. We give an application of this strong convergence to the Jacobi process.
History
Publication status
- Published
Journal
Probability Theory and Related FieldsISSN
0178-8051Publisher
Springer VerlagExternal DOI
Issue
1-2Volume
170Page range
49-93Department affiliated with
- Mathematics Publications
Research groups affiliated with
- Probability and Statistics Research Group Publications
Full text available
- No
Peer reviewed?
- Yes
Legacy Posted Date
2019-03-25Usage metrics
Categories
No categories selectedKeywords
Licence
Exports
RefWorks
BibTeX
Ref. manager
Endnote
DataCite
NLM
DC