On the concentration of eigenvalues of random symmetric matrices

Noga Alon; Michael Krivelevich; Van H. Vu

doi:10.1007/BF02785860

On the concentration of eigenvalues of random symmetric matrices

Noga Alon
, Michael Krivelevich
, Van H. Vu

Research output: Contribution to journal › Article › peer-review

80 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 language	English (US)
Pages (from-to)	259-267
Number of pages	9
Journal	Israel Journal of Mathematics
Volume	131
DOIs	https://doi.org/10.1007/BF02785860
State	Published - 2002
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/BF02785860

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title = "On the concentration of eigenvalues of random symmetric matrices",

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.",

author = "Noga Alon and Michael Krivelevich and Vu, \{Van H.\}",

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doi = "10.1007/BF02785860",

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volume = "131",

pages = "259--267",

journal = "Israel Journal of Mathematics",

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T1 - On the concentration of eigenvalues of random symmetric matrices

AU - Alon, Noga

AU - Krivelevich, Michael

AU - Vu, Van H.

PY - 2002

Y1 - 2002

N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/0036459716

UR - https://www.scopus.com/pages/publications/0036459716#tab=citedBy

U2 - 10.1007/BF02785860

DO - 10.1007/BF02785860

M3 - Article

AN - SCOPUS:0036459716

SN - 0021-2172

VL - 131

SP - 259

EP - 267

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

ER -

On the concentration of eigenvalues of random symmetric matrices

Abstract

All Science Journal Classification (ASJC) codes

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