On the multifractal analysis of the branching random walk in R^d

TL;DR

This paper proves that the multifractal formalism holds almost surely for R^d-valued branching random walks within the core domain, advancing understanding of their complex scaling behaviors.

Contribution

It establishes the almost sure validity of the multifractal formalism for R^d-valued branching random walks in the entire natural convex domain.

Findings

Multifractal formalism is valid almost surely in the studied setting.

Results apply to the whole relative interior of the convex domain.

Advances understanding of the multifractal structure of branching random walks.

Abstract

We establish the almost sure validity of the multifractal formalism for R^d-valued branching random walks on the whole relative interior of the natural convex domain of study.