Lacunarity Exponents

TL;DR

This paper introduces the concept of lacunarity exponents to characterize the uneven distribution of matter in physical processes, providing analytical expressions and explaining their widespread occurrence.

Contribution

It defines lacunarity exponents, proposes a mechanism for their prevalence, and derives analytical formulas in simple models, advancing understanding of matter distribution fluctuations.

Findings

Lacunarity exponents characterize matter density fluctuations.

A mechanism explains the widespread occurrence of power-law distributions.

Analytical expressions for lacunarity exponents are derived in simple models.

Abstract

Many physical processes result in very uneven, apparently random, distributions of matter, characterized by fluctuations of the local density over orders of magnitude. The density of matter in the sparsest regions can have a power-law distribution, with an exponent that we term the lacunarity exponent. We discuss a mechanism which explains the wide occurrence of these power laws, and give analytical expressions for the exponent in some simple models.