Strong Local Nondeterminism and Exact Modulus of Continuity for Isotropic Gaussian Random Fields on Compact Two-Point Homogeneous Spaces

TL;DR

This paper investigates the sample path properties of isotropic Gaussian fields on compact two-point homogeneous spaces, establishing strong local nondeterminism and an exact uniform modulus of continuity based on spectral analysis.

Contribution

It introduces the property of strong local nondeterminism for these fields and derives an exact modulus of continuity, advancing understanding of their sample path behavior.

Findings

Proves strong local nondeterminism for isotropic Gaussian fields.

Establishes an exact uniform modulus of continuity for sample paths.

Links spectral properties to path regularity.

Abstract

This paper is concerned with sample path properties of isotropic Gaussian fields on compact two-point homogeneous spaces. In particular, we establish the property of strong local nondeterminism of an isotropic Gaussian field based on the high-frequency behavior of its angular power spectrum, and then exploit this result to establish an exact uniform modulus of continuity for its sample paths.