Poisson point processes: Large deviation inequalities for the convex distance

TL;DR

This paper introduces a convex distance analogue for Poisson point processes and establishes a large deviation inequality, extending Talagrand's inequalities to this stochastic setting.

Contribution

It defines a new convex distance for Poisson processes and proves a large deviation inequality, advancing the theoretical understanding of stochastic geometry.

Findings

Established a convex distance analogue for Poisson processes

Proved a large deviation inequality for the new distance

Extended Talagrand's inequalities to Poisson point processes

Abstract

An analogue of Talagrand's convex distance for binomial and Poisson point processes is defined. A corresponding large deviation inequality is proved.