Conditional measures for Pfaffian point processes: conditioning on a bounded domain

TL;DR

This paper derives explicit formulas for the kernels of conditioned Pfaffian point processes, including Palm measures and measures conditioned on configurations in bounded domains, enhancing understanding of their structure.

Contribution

It provides explicit formulas for the kernels of Palm measures and conditioned measures of Pfaffian point processes, advancing the theoretical understanding of their structure.

Findings

Explicit kernels for Palm measures derived

Formulas for conditioned measures on bounded domains obtained

Enhanced understanding of Pfaffian point process structure

Abstract

For a Pfaffian point process we show that its Palm measures, its normalised compositions with multiplicative functionals, and its conditional measures with respect to fixing the configuration in a bounded subset are Pfaffian point processes whose kernels we find explicitly.