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math.PR2024★ 1 cited
On Marginal Stability in Low Temperature Spherical Spin Glasses
Mark Sellke
We show marginal stability of near-ground states in spherical spin glasses is equivalent to full replica symmetry breaking at zero temperature near overlap . This connection has…
math.PR2024
Free Energy Universality of Spherical Spin Glasses
Mehtaab Sawhney, Mark Sellke
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…
math.PR2024
Localization of Random Surfaces with Monotone Potentials and an FKG-Gaussian Correlation Inequality
Mark Sellke
The seminal 1975 work of Brascamp-Lieb-Lebowitz initiated the rigorous study of Ginzberg-Landau random surface models. It was conjectured therein that fluctuations are localized on…