On a zero-one law for the norm process of transient random walk

TL;DR

This paper proves a zero-one law for the norm process of transient random walks, utilizing invariance principles and a limit version of Jeulin's lemma to establish the result.

Contribution

It introduces a zero-one law for the norm process of transient random walks, extending understanding of their asymptotic behavior.

Findings

Zero-one law established for the norm process

Invariance principle for local times proved

Limit version of Jeulin's lemma developed

Abstract

A zero-one law of Engelbert--Schmidt type is proven for the norm process of a transient random walk. An invariance principle for random walk local times and a limit version of Jeulin's lemma play key roles.