Eigenvalue results for large scale random Vandermonde matrices with unit complex entries

Gabriel H. Tucci, Philip A. Whiting

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)

Abstract

This paper centers on the limit eigenvalue distribution for random Vandermonde matrices with unit magnitude complex entries. The phases of the entries are chosen independently and identically distributed from the interval [-π,π]. Various types of distribution for the phase are considered and we establish the existence of the empirical eigenvalue distribution in the large matrix limit on a wide range of cases. The rate of growth of the maximum eigenvalue is examined and shown to be no greater than O(log N) and no slower than O(log N/log log N) where n is the dimension of the matrix. Additional results include the existence of the capacity of the Vandermonde channel (limit integral for the expected log determinant).

Original languageEnglish
Article number5773061
Pages (from-to)3938-3954
Number of pages17
JournalIEEE Transactions on Information Theory
Volume57
Issue number6
DOIs
Publication statusPublished - Jun 2011
Externally publishedYes

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