On the Characteristic Polynomial of the Eigenvalue Moduli of Random Normal Matrices
We study the characteristic polynomial pn(x)=∏j=1n(|zj|-x) where the zj are drawn from the Mittag–Leffler ensemble, i.e. a two-dimensional determinantal point process which generalizes the Ginibre point process. We obtain precise large n asymptotics for the moment generating function E[euπIm\,lnpn(r)eaRe\,lnpn(r)], in the case where r is in the bulk, u ϵ R and a ϵ N. This expectation involves an n