Published January 2015
| Version Submitted
Journal Article
Open
Local spectrum of truncations of Kronecker products of Haar distributed unitary matrices
Creators
Abstract
We address the local spectral behavior of the random matrix Π_1U^(⊗k)Π_2U^(⊗k∗)Π_1 where U is a Haar distributed unitary matrix of size n × n, the factor k is at most c0lgn for a small constant c_0 > 0, and Π_1, Π_2 are arbitrary projections on ℓ^n^k_2of ranks proportional to n^k. We prove that in this setting the k-fold Kronecker product behaves similarly to the well-studied case when k = 1.
Additional Information
© 2015 World Scientific Publishing Company. Received 2 June 2014; Accepted 21 January 2015; Published 27 February 2015. The authors thank the two reviewers for many helpful comments. B. Farrell was partially supported by Joel A. Tropp under ONR awards N00014-08-1-0883 and N00014-11-1002 and a Sloan Research Fellowship. R. R. Nadakuditi was partially supported by an ONR Young Investigator Award N000141110660, an AFOSR Young Investigator Award FA9550-12-1-0266, a ARO MURI grant W911NF-11-1-0391 and NSF CCF1116115.Attached Files
Submitted - 1311.6783v1.pdf
Files
1311.6783v1.pdf
Additional details
Identifiers
- Eprint ID
- 70283
- DOI
- 10.1142/S201032631550001X
- Resolver ID
- CaltechAUTHORS:20160912-152352385
Related works
- Describes
- 10.1142/S201032631550001X (DOI)
- http://arxiv.org/abs/1311.6783 (URL)
Funding
- Office of Naval Research (ONR)
- N00014-08-1-0883
- Office of Naval Research (ONR)
- N00014-11-1002
- Alfred P. Sloan Foundation
- Office of Naval Research (ONR)
- N00014-11-10660
- Air Force Office of Scientific Research (AFOSR)
- FA9550-12-1-0266
- Army Research Office (ARO)
- W911NF-11-1-0391
- NSF
- CCF-1116115
Dates
- Created
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2016-09-13Created from EPrint's datestamp field
- Updated
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2021-11-11Created from EPrint's last_modified field