2012/11/15 by Ghosh, Subhro
#FOS: Mathematics #FOS: Physical sciences #Probability (math.PR) #Statistical Mechanics (cond-mat.stat-mech)
paper · doi:10.48550/arxiv.1211.3506
Let Π be a translation invariant point process on the complex plane \C and let \D ⊂ \C be a bounded open set whose boundary has zero Lebesgue measure. We study the conditional distribution of the points of Π inside \D given the points outside \D. When Π is the Ginibre ensemble or the Gaussian zero process, it been shown in \citeGP that this conditional distribution is mutually absolutely continuous with the Lebesgue measure on its support. In this paper, we refine the result in \citeGP 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.