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Free Energy Universality of Spherical Spin Glasses
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abstract
We prove the free energy and ground state energy of spherical spin glasses are universal under the minimal moment assumptions. Previously such universality was known only for Ising spin glasses and random symmetric matrices, the latter being a celebrated result of Bai--Yin. Our methods extend to $\ell^q$ balls for $q>2$, thus resolving a conjecture of Chen-Sen, and to tensor PCA.
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Regularized Bulk Universality versus Bounded-Disorder Nonuniversality for Annealed Complexity of Spherical $p$-Spin Landscapes
For spherical p-spin models, moment matching guarantees universality of regularized bulk complexity but not of the unregularized annealed critical-point count, which can be strictly larger for bounded smooth disorder.
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