Behavior of the minimum singular value of a random Vandermonde matrix

Gabriel H. Tucci*, Philip A. Whiting

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference proceeding contributionpeer-review

Abstract

In this work we examine the behavior of the minimum singular value of random Vandermonde matrices. In particular, we prove that the minimum singular value s 1(N) is at most N exp(-C√N) where N is the dimension of the matrix and C is a constant. Furthermore, the value of the constant C is determined explicitly. The main result is obtained in two different ways. One approach uses techniques from stochastic processes and in particular, a construction related to the Brownian bridge. The other one is a more direct analytical approach involving combinatorics and complex analysis. As a consequence, we obtain a lower bound on the maximum absolute value of a random polynomial on the unit circle, which may be of independent mathematical interest.

Original languageEnglish
Title of host publication2012 IEEE international symposium on information theory proceedings, ISIT 2012
Place of PublicationPiscataway, NJ
PublisherInstitute of Electrical and Electronics Engineers (IEEE)
Pages2441-2445
Number of pages5
ISBN (Electronic)9781467325790
ISBN (Print)9781467325806
DOIs
Publication statusPublished - 2012
Externally publishedYes
Event2012 IEEE International Symposium on Information Theory, ISIT 2012 - Cambridge, MA, United States
Duration: 1 Jul 20126 Jul 2012

Other

Other2012 IEEE International Symposium on Information Theory, ISIT 2012
CountryUnited States
CityCambridge, MA
Period1/07/126/07/12

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