# Random interlacements for vertex-reinforced jump processes

## TL;DR

This paper introduces a new framework called random interlacements for analyzing transient vertex-reinforced jump processes on general graphs, showing convergence of finite subgraph processes to this new model.

## Contribution

The paper develops the concept of random interlacements for vertex-reinforced jump processes and proves their convergence on increasing finite subgraphs with wired boundary conditions.

## Key findings

- Convergence of vertex-reinforced jump processes on finite subgraphs to random interlacements.
- Extension of random interlacement theory to vertex-reinforced jump processes.
- Framework applicable to general graphs.

## Abstract

We introduce random interlacements for transient vertex-reinforced jump processes on a general graph $G$. Using increasing finite subgraphs $G_n$ of $G$ with wired boundary conditions, we show convergence of the vertex-reinforced jump process on $G_n$ observed in a finite window to the random interlacement observed in the same window.