| Zusammenfassung: | We study the limiting spectral measure of large symmetric random matrices of linear algebraic structure. For Hankel and Toeplitz matrices generated by i.i.d. random variables $\{X_{k}\}$ of unit variance, and for symmetric Markov matrices generated by i.i.d. random variables $\{X_{ij}\}_{j>i}$ of zero mean and unit variance, scaling the eigenvalues by $\sqrt{n}$ we prove the almost sure, weak convergence of the spectral measures to universal, nonrandom, symmetric distributions $\gamma _{H}$ , $\gamma _{M}$ and $\gamma _{T}$ of unbounded support. The moments of $\gamma _{H}$ and $\gamma _{T}$ are the sum of volumes of solids related to Eulerian numbers, whereas $\gamma _{M}$ has a bounded smooth density given by the free convolution of the semicircle and normal densities. For symmetric Markov matrices generated by i.i.d. random variables $\{X_{ij}\}_{j>i}$ of mean m and finite variance, scaling the eigenvalues by n we prove the almost sure, weak convergence of the spectral measures to the atomic measure at -m. If m = 0, and the fourth moment is finite, we prove that the spectral norm of ${\bf M}_{n}$ scaled by $\sqrt{2n\,{\rm log}\,n}$ log n converges almost surely to 1.
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