H\"older Conditions of Local Times and Exact Moduli of non-differentiability for Spherical Gaussian fields

TL;DR

This paper studies the local times and non-differentiability properties of spherical Gaussian fields, extending Gaussian local time analysis methods to the spherical setting using recent strong local nondeterminism results.

Contribution

It introduces a novel approach to analyze local times and moduli of nondifferentiability for spherical Gaussian fields, leveraging recent advances in strong local nondeterminism.

Findings

Established H"older conditions for local times

Derived exact moduli of non-differentiability

Extended Gaussian local time methods to spherical fields

Abstract

This paper investigate the local times and modulus of nondifferentiability of the spherical Gaussian random fields. We extend the methods for studying the local times of Gaussian to the spherical setting. The new main ingredient is the property of strong local nondeterminism established recently in Lan et al (2018).