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A126848
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Arises in lower bound of the spectral norm of n X n symmetric random matrices.
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0
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2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14
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OFFSET
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1,1
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COMMENTS
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Abstract: "We show that the spectral radius of an N times N random symmetric matrix with i.i.d. bounded centered but non-symmetrically 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.
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LINKS
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FORMULA
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a(n) = floor(2*n*(n^(-6/11))).
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EXAMPLE
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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).
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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