Rigorous theorems establish zero-temperature glassy signatures in the finite-dimensional Edwards-Anderson model including perturbation-sensitive ground states, fractal droplet interfaces, and low-energy macroscopic excitations.
Tight Lipschitz Hardness for Optimizing Mean Field Spin Glasses
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Online algorithms achieve multiplicative approximation r^{1/(r-1)} for maximum independent sets in dense r-uniform ER hypergraphs and (max γ_i)^{-1/(r-1)} for balanced sets in r-partite versions, with matching lower bounds.
Presents the first iterative spectral algorithm for near-optimal solutions to random quadratic optimization over the hypercube, resolving Subag's conjecture via potential Hessian ascent and SDE approximation.
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Spin glass phase at zero temperature in the Edwards-Anderson model
Rigorous theorems establish zero-temperature glassy signatures in the finite-dimensional Edwards-Anderson model including perturbation-sensitive ground states, fractal droplet interfaces, and low-energy macroscopic excitations.
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Algorithmic Phase Transition for Large Independent Sets in Dense Hypergraphs
Online algorithms achieve multiplicative approximation r^{1/(r-1)} for maximum independent sets in dense r-uniform ER hypergraphs and (max γ_i)^{-1/(r-1)} for balanced sets in r-partite versions, with matching lower bounds.
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Potential Hessian Ascent: The Sherrington-Kirkpatrick Model
Presents the first iterative spectral algorithm for near-optimal solutions to random quadratic optimization over the hypercube, resolving Subag's conjecture via potential Hessian ascent and SDE approximation.