Integral means spectrum of random conformal snowflakes

TL;DR

This paper constructs random conformal snowflakes to improve lower bounds on the universal integral means spectrum, achieving estimates close to the conjectured values and advancing understanding of fractal boundary behavior.

Contribution

Introduces new random conformal snowflakes that significantly improve lower bounds on the universal spectrum, approaching conjectured values.

Findings

New estimates are within 5-10% of the conjectured spectrum.

Constructed snowflakes exhibit large integral means spectrum at various points.

Results represent a substantial improvement over previous lower bounds.

Abstract

In this paper we construct random conformal snowflakes with large integral means spectrum at different points. These new estimates are significant improvement over previously known lower bound of the universal spectrum. Our estimates are within 5-10 percent from the conjectured value of the universal spectrum.