On the percolative properties of the intersection of two independent interlacements

TL;DR

This paper investigates the percolative behavior of the intersection of two independent random interlacements and its complement, establishing phase transitions and percolation properties in high dimensions.

Contribution

It proves the existence of non-trivial phase transitions for the intersection and its complement, and shows percolation occurs in high dimensions.

Findings

Existence of phase transitions for the intersection and its complement

Asymptotic results about phase curves

Percolation in high dimensions

Abstract

We prove the existence of non-trivial phase transitions for the intersection of two independent random interlacements and the complement of the intersection. Some asymptotic results about the phase curves are also obtained. Moreover, we show that at least one of these two sets percolates in high dimensions.