A Construction of the Stable Web

TL;DR

This paper introduces a process on coalescing stable paths and proves its convergence for coalescing stable random walks on the integer lattice, advancing understanding of their limiting behavior.

Contribution

It constructs a new process on coalescing stable paths and establishes convergence results, extending prior work on coalescing random walks.

Findings

Established convergence of coalescing stable random walks to a limiting process

Developed a new process on coalescing cadlag stable paths

Extended results to the space of coalescing paths

Abstract

We provide a process on the space of coalescing cadlag stable paths and show convergence in the appropriate topology for coalescing stable random walks on the integer lattice.