Central limit theorem for the complex eigenvalues of Gaussian random matrices

We establish a central limit theorem for the counting function of the eigenvalues of a matrix of real Gaussian random variables.Comment: 11 page

Big flip graphs and their automorphism groups

In this paper, we study the relationship between the mapping class group of an infinite-type surface and the simultaneous flip graph, a variant of the flip graph for infinite-type surfaces defined by Fossas and Parlier [6]. We show that the extended mapping class group is isomorphic to a proper subgroup of the automorphism group of the flip graph, unlike in the finite-type case. This shows that Ivanov\u27s metaconjecture, which states that any “sufficiently rich" object associated to a finite-type surface has the extended mapping class group as its automorphism group, does not extend to simultaneous flip graphs of infinite-type surfaces