The Expected Eigenvalue Distribution of a Large Regular Graph
نویسندگان
چکیده
Let X,, X,,. be a sequence of regular graphs with degree ~a2 such that n(X,)cc and ck(X,)/n(X,)-0 as i -cc for each ka3, where n(X,) is the order of Xi, and ck( X,) is the number of k-cycles in Xi. We determine the limiting probability density f(x) for the eigenvalues of X, as i-cc. It turns out that i o/4(“-1)-x” f(x)= 2n(u”_x’) for IrlG2JFi, IO otherwise It is further shown that f(x) is the expected eigenvalue distribution for every large randomly chosen labeled regular graph with degree u.
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