Laplacian operator on statistical manifold

TL;DR

This paper introduces a novel Laplacian operator on statistical manifolds, called the vector Laplacian, which integrates the Amari-Chentsov tensor and has applications in heat kernel analysis.

Contribution

It defines the vector Laplacian on statistical manifolds and derives a formula, extending geometric analysis tools to information geometry.

Findings

Derived a formula for the vector Laplacian.

Presented two applications involving the heat kernel.

Enhanced understanding of geometric structures in statistical manifolds.

Abstract

In this paper, we define a Laplacian operator on a statistical manifold, called the vector Laplacian. This vector Laplacian incorporates information from the Amari-Chentsov tensor. We derive a formula for the vector Laplacian. We also give two applications using the heat kernel associated with the vector Laplacian.