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.
"A connection between the Ghirlanda–Guerra identities and ultrametricity." Ann. Probab. 38 (1) 327 - 347, January 2010. https://doi.org/10.1214/09-AOP484