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We consider ensembles of real symmetric band matrices with entries drawn from an infinite sequence of exchangeable random variables, as far as the symmetry of the matrices permits. In general the entries of the upper triangular parts of these matrices are correlated and no smallness or sparseness of these correlations is assumed. It is shown that the eigenvalue distribution measures still converge to a semicircle but with random scaling. We also investigate the asymptotic behavior of the corresponding $ell_2$-operator norms. The key to our analysis is a generalisation of a classic result by de Finetti that allows to represent the underlying probability spaces as averages of Wigner band ensembles with entries that are not necessarily centred. Some of our results appear to be new even for such Wigner band matrices.
We derive concentration inequalities for functions of the empirical measure of large random matrices with infinitely divisible entries and, in particular, stable ones. We also give concentration results for some other functionals of these random matr
We study the singularity probability of random integer matrices. Concretely, the probability that a random $n times n$ matrix, with integer entries chosen uniformly from ${-m,ldots,m}$, is singular. This problem has been well studied in two regimes:
For an $ntimes n$ matrix $A_n$, the $rto p$ operator norm is defined as $$|A_n|_{rto p}:= sup_{boldsymbol{x} in mathbb{R}^n:|boldsymbol{x}|_rleq 1 } |A_nboldsymbol{x}|_pquadtext{for}quad r,pgeq 1.$$ For different choices of $r$ and $p$, this norm cor
Gibbs-type random probability measures and the exchangeable random partitions they induce represent an important framework both from a theoretical and applied point of view. In the present paper, motivated by species sampling problems, we investigate
Consider a population of individuals belonging to an infinity number of types, and assume that type proportions follow the two-parameter Poisson-Dirichlet distribution. A sample of size n is selected from the population. The total number of different