Russo's formula for random interlacements

TL;DR

This paper derives explicit formulas for how the probability of increasing events in the random interlacements model changes with the model's intensity parameter, providing insights into the model's sensitivity.

Contribution

It introduces explicit expressions for the derivative of increasing event probabilities in the random interlacements model with respect to intensity.

Findings

Derived explicit formulas for probability derivatives

Applied formulas to finite subsets of the lattice

Enhanced understanding of model sensitivity to parameters

Abstract

In this paper we obtain a couple of explicit expressions for the derivative of the probability of an increasing event in the random interlacements model. The event is supported in a finite subset of the lattice, and the derivative is with respect to the intensity parameter of the model.