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Register a new userOn the gap of finite metric spaces of p-negative type
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Authors
Reinhard Wolf
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Let (X,d) be a metric space of p-negative type. Recently I. Doust and A. Weston introduced a quantification of the p-negative type property, the so called gap {Gamma} of X. This talk introduces some formulas for the gap {Gamma} of a finite metric space of strict p-negative type and applies them to evaluate {Gamma} for some concrete finite metric spaces.
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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.
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