Estimating the gap of finite metric spaces of strict p-negative type

TL;DR

This paper investigates the spectral properties and gap bounds of finite metric spaces with strict p-negative type, providing estimations and applications to ultrametric spaces.

Contribution

It introduces new bounds for the gap of finite metric spaces of strict p-negative type and explores spectral characteristics related to p-distance matrices.

Findings

Derived upper and lower bounds for the gap of finite metric spaces

Provided estimations for the gap under glueing constructions

Applied results to finite ultrametric spaces

Abstract

Let (X,d) be a finite metric space. This paper first discusses the spectrum of the p-distance matrix of a finite metric space of p-negative type and then gives upper and lower bounds for the so called gap of a finite metric space of strict p-negative type. Furthermore estimations for the gap under a certain glueing construction for finite metric spaces are given and finally be applied to finite ultrametric spaces.