Dirichlet fractional Gaussian fields on the Sierpinski gasket and their discrete graph approximations

TL;DR

This paper introduces Dirichlet fractional Gaussian fields on the Sierpinski gasket and demonstrates their convergence from discrete graph-based fields, advancing understanding of fractal-based Gaussian processes.

Contribution

It defines fractional Gaussian fields on fractals and proves their approximation by discrete graph models, bridging continuous and discrete fractal analysis.

Findings

Dirichlet fractional Gaussian fields are well-defined on the Sierpinski gasket.

These fields can be obtained as limits of fractional Gaussian fields on approximating graphs.

The work connects discrete graph models with continuous fractal fields.

Abstract

We define and study the Dirichlet fractional Gaussian fields on the Sierpinski gasket and show that they are limits of fractional discrete Gaussian fields defined on the sequence of canonical approximating graphs.