A connection between the Ghirlanda--Guerra identities and ultrametricity
classification
🧮 math.PR
math-phmath.MP
keywords
ghirlanda--guerraidentitiesultrametricityconditionconnectionconsiderdefiniteelements
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We consider a symmetric positive definite weakly exchangeable infinite random matrix and show that, under the technical condition that its elements take a finite number of values, the Ghirlanda--Guerra identities imply ultrametricity.
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