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math.PR2022★ 1 cited
Existence of the free energy for heavy-tailed spin glasses
Aukosh Jagannath, Patrick Lopatto
We study the free energy of a mean-field spin glass whose coupling distribution has power law tails. Under the assumption that the couplings have infinite variance and finite mean,…
math.PR2022
Mobility Edge for Lévy Matrices
Amol Aggarwal, Charles Bordenave, Patrick Lopatto
Lévy matrices are symmetric random matrices whose entry distributions lie in the domain of attraction of an -stable law. For , predictions from the physics literature sugg…