Intersection local times for interlacements

TL;DR

This paper introduces renormalized intersection local times for random interlacements of Lévy processes in multi-dimensional space and establishes an isomorphism theorem linking these local times with Wick polynomials.

Contribution

It defines a new concept of renormalized intersection local times for Lévy process interlacements and proves a novel isomorphism theorem connecting these with Wick polynomials.

Findings

Defined renormalized intersection local times for Lévy process interlacements

Proved an isomorphism theorem relating local times to Wick polynomials

Established foundational results for analysis of Lévy process interlacements

Abstract

We define renormalized intersection local times for random interlacements of L\'evy processes in R^{d} and prove an isomorphism theorem relating renormalized intersection local times with associated Wick polynomials.