Local dependencies in random fields via a Bonferroni-type inequality

TL;DR

This paper introduces a Bonferroni-type inequality that aids in analyzing large deviations and limit theorems for sums of random fields, especially with heavy tails or compound Poisson limits.

Contribution

It provides a new inequality applicable to studying large deviations and limit theorems for random fields with negligible small values, covering stable and compound Poisson limits.

Findings

Useful for large deviation analysis of random fields

Applicable to stable limits with heavy tails

Handles compound Poisson limits of 0-1 variables

Abstract

We provide an inequality which is a useful tool in studying both large deviation results and limit theorems for sums of random fields with "negligible" small values. In particular, the inequality covers cases of stable limits for random variables with heavy tails and compound Poisson limits of $0-1$ random variables.