

A126848


Arises in lower bound of the spectral norm of n X n symmetric random matrices.


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OFFSET

1,1


COMMENTS

Abstract: "We show that the spectral radius of an N times N random symmetric matrix with i.i.d. bounded centered but nonsymmetrically distributed entries is bounded from below by 2 *sigma  o(N^{6/11+\epsilon}), where sigma^2 is the variance of the matrix entries and epsilon is an arbitrary small positive number. Combining with our previous result from [6], this proves that for any epsilon > 0, one has A_N =2*sigma + o(N^{6/11+epsilon}) with probability going to 1 as N goes to infinity." In this sequence, we computer a lower bound under the artificial assumption that sigma = n. Records for a(n) are for n = 1, 3, 5, 8, 12, 16, 22, 28, 35, 43, 52, 62, 73.


LINKS



FORMULA

a(n) = floor(2*n*(n^(6/11))).


EXAMPLE

a(10) = 5 because 5 = floor(2 * 10 * (10^((6/11))) = floor(5.69607174).
a(100) = 16 = floor(2 * 100 * (100^((6/11)) = floor(16.2226166).
a(1000) = 46 = floor(2 * 1000 * (1000^((6/11)) = floor(46.202594).
a(10000) = 131 = floor(2 * 10000 * (10000^((6/11)) = floor(131.586645).
a(100000) = 374 = floor(2 * 100000 * (1000000^((6/11)) = floor(374.763485).
a(1000000) = 1067 = floor(2 * 1000000 * (1000000^((6/11)) = floor(1067.33985).


CROSSREFS



KEYWORD

easy,nonn


AUTHOR



STATUS

approved



