We classify SU(3) gauge field configurations in different topological sectors by the smearing technique. In each sector we compute the distribution of low lying eigenvalues of the staggered Dirac operator. In all sectors we find perfect agreement with the predictions for the sector of topological charge zero. The smallest Dirac operator eigenvalues of staggered fermions at presently realistic l...

We investigate spacing statistics for ensembles of various real random matrices where the matrixelements have various Probability Distribution Function (PDF: f(x)) including Gaussian. For two modifications of 2 × 2 matrices with various PDFs, we derived that spacing distribution p(s) of adjacent energy eigenvalues are distinct. Nevertheless, they show the linear level repulsion near s = 0 as αs...

Let U be a real n x n matrix whose entries uij are random variables, and let A and B be fixed n x n real symmetric matrices. Statisticians (e.g., see [OU]) have been interested in the distribution of the eigenvalues d l , . . . , O n of the matrix AUBUt, where denotes transpose. Of particular interest are the quantities tr((AU = C 0; for k = 1,2,. . . , since these determine the eigenvalues. Mo...

We examine the empirical distribution of the eigenvalues and the eigenvectors of adjacency matrices of sparse regular random graphs. We find that when the degree sequence of the graph slowly increases to infinity with the number of vertices, the empirical spectral distribution converges to the semicircle law. Moreover, we prove concentration estimates on the number of eigenvalues over progressi...

We study the asymptotic distribution of eigenvalues of integral operators Tk defined by kernels k which belong to Triebel-Lizorkin function space Fσ pu(F qv) by using the factorization theorem and the Weyl numbers xn. We use the relation between Triebel-Lizorkin space Fσ pu(Ω) and Besov space Bτ pq(Ω) and the interpolation methods to get an estimation for the distribution of eigenvalues in Lizo...

Consider the ensemble of real symmetric Toeplitz matrices whose entries are i.i.d random variables chosen from a fixed probability distribution p of mean 0, variance 1 and finite higher moments. Previous work [BDJ, HM] showed that the limiting spectral measures (the density of normalized eigenvalues) converge weakly and almost surely to a universal distribution almost that of the Gaussian, inde...

τ(n)e(nz). The two equations were proven for τ(n) by Mordell, using what are now known as the Hecke operators. The inequality was proven by Deligne as a consequence of his proof of the Weil conjectures. Those results determine everything about af (n) except for the distribution of the af (p) ∈ [−2, 2]. Define θf (p) ∈ [0, π] by af (p) = 2 cos θf (p). It is conjectured that for each f the θf (p)...