On the concentration of eigenvalues of random symmetric matrices

Noga Alon, Michael Krivelevich, Van H. Vu

Research output: Contribution to journalArticlepeer-review

70 Scopus citations

Abstract

It is shown that for every 1 ≤ s ≤ n, the probability that the s-th largest eigenvalue of a random symmetric n-by-n matrix with independent random entries of absolute value at most I deviates from its median by more than t is at most 4e-t2/32s2. The main ingredient in the proof is Talagrand's Inequality for concentration of measure in product spaces.

Original languageEnglish (US)
Pages (from-to)259-267
Number of pages9
JournalIsrael Journal of Mathematics
Volume131
DOIs
StatePublished - 2002

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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