Normal limit theorems for symmetric random matrices (Q1272367)

The author studies the limiting behavior of \(N\)-dimensional symmetric random matrices \(A_N\) whose probability distribution is invariant under the orthogonal transformations. The results include limiting theorems for \(k\times k\) submatrices of \(A_N\) and proofs of the convergence of partial sums of diagonal elements of \(A_N\) to the Brownian motion, in the limit \(N\to\infty\).