Conditional measures of generalized Ginibre point processes

TL;DR

This paper characterizes the conditional measures of generalized Ginibre point processes as orthogonal polynomial ensembles with explicit weights, simplifying understanding especially for radially-symmetric cases like the classical Ginibre process.

Contribution

It provides explicit formulas for the conditional measures of generalized Ginibre point processes, advancing the theoretical understanding of their structure.

Findings

Conditional measures are orthogonal polynomial ensembles with explicit weights.

Special case formulas for radially-symmetric determinantal point processes.

Simplified description for classical Ginibre point process.

Abstract

The main result of this paper is that conditional measures of generalized Ginibre point processes, with respect to the configuration in the complement of a bounded open subset on $\mathbb{C}$, are orthogonal polynomial ensembles with weights found explicitly. An especially simple formula for conditional measures is obtained in the particular case of radially-symmetric determinantal point processes, including the classical Ginibre point process.