On the concentration of eigenvalues of random symmetric matrices
On the concentration of eigenvalues of random symmetric matrices
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DOI：
10.1007/bf02785860
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发表时间：
2002-01-01
影响因子：
1
通讯作者：
Vu, VH
中科院分区：
文献类型：
--
作者：
Alon, N;Krivelevich, M;Vu, VH
证明了对于每1小于或等于S小于或等于n，具有至多1个独立的绝对值随机项的随机对称n×n矩阵的S第个最大特征值偏离其中值超过t的概率至多为4e(-T2)/32(S2)。证明中的主要内容是关于乘积空间中的测度集中的TALAGRAND不等式。
It is shown that for every 1 less than or equal to s less than or equal to 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 1 deviates from its median by more than t is at most 4e(-t2) /32(s2). The main ingredient in the proof is Talagrand's Inequality for concentration of measure in product spaces.