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 | |
State | Published - 2002 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- General Mathematics