%0 Journal Article
%T Rigidity and Tolerance in Gaussian zeroes and Ginibre eigenvalues: quantitative estimates
%A Subhro Ghosh
%J Mathematics
%D 2012
%I arXiv
%X Let $\Pi$ be a translation invariant point process on the complex plane $\C$ and let $\D \subset \C$ be a bounded open set whose boundary has zero Lebesgue measure. We study the conditional distribution of the points of $\Pi$ inside $\D$ given the points outside $\D$. When $\Pi$ is the Ginibre ensemble or the Gaussian zero process, it been shown in \cite{GP} that this conditional distribution is mutually absolutely continuous with the Lebesgue measure on its support. In this paper, we refine the result in \cite{GP} to show that the conditional density is, roughly speaking, comparable to a squared Vandermonde density. In particular, this shows that even under spatial conditioning, the points exhibit repulsion which is quadratic in their mutual separation.
%U http://arxiv.org/abs/1211.3506v1