Talagrand's critical Sherrington-Kirkpatrick overlap conjecture

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This event attributed to Brice Huang

This event attributed to Hang Du

This event attributed to GPT-5.6 Pro

Du and Huang's companion paper on critical SK free-energy fluctuations, whose ideas this work extends evidence for this event

Dey and Kang (arXiv:2603.05636) - quotes Conjecture 11.7.5 as open, five months before this proof evidence for this event

Talagrand's critical Sherrington-Kirkpatrick overlap conjecture evidence for this event

Talagrand's Conjecture 11.7.5 is resolved affirmatively for the critical Ising Sherrington-Kirkpatrick model: $N^{2/3}\mathbb{E}\langle R_{1,2}^2\rangle$ converges to a positive finite constant. The paper proves substantially more, showing that the entire quenched distribution of $N^{1/3}R_{1,2}$ converges to an explicit random probability measure defined from the reflected $\mathrm{Airy}_1$ point process. The same limiting distribution and second-moment constant are obtained for the spherical SK model. This does not resolve the broader low-temperature overlap structure of the SK model. parent of this event

VibeMathed record: Talagrand's critical Sherrington-Kirkpatrick overlap conjecture evidence for this event

Talagrand's critical Sherrington-Kirkpatrick overlap conjecture parent of this event