Measure on gauge invariant symmetric norms

TL;DR

This paper introduces gauge invariant symmetric random norms, constructs such norms on the plane, extends them to higher dimensions, and numerically analyzes their unit spheres.

Contribution

It develops the theory of gauge invariant symmetric random norms, including their construction, extension to higher dimensions, and numerical analysis of their properties.

Findings

Constructed gauge invariant symmetric random norms on the plane

Extended these norms to higher (including infinite) dimensions

Numerically computed unit spheres of expected norms in 2D and 3D

Abstract

The concept of a gauge invariant symmetric random norm is elaborated in this paper. We introduce norm processes and show that this kind of stochastic processes are closely related to gauge invariant symmetric random norms. We construct a gauge invariant symmetric random norm on the plain. We define two different extensions of these random norms to higher (even infinite) dimensions. We calculate numerically unit spheres of expected norms in two and three dimensions for the constructed random norm.