Brice Huang

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20242026

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math.PR2026

Overlap distribution of the critical Sherrington-Kirkpatrick model

Hang Du, Brice Huang

We study the distribution of the two-replica overlap $R_{1, 2}$ in the Ising and spherical Sherrington-Kirkpatrick models at the critical inverse temperature $β = 1$ . Our main result…

math.PR2026

Fluctuations of the Sherrington-Kirkpatrick free energy at critical temperature

Hang Du, Brice Huang

We consider the Sherrington-Kirkpatrick spin glass model at the critical inverse temperature $I^^{2} = 1$ with zero external field. We prove that the free energy $F_{N} = F_{N, I^^{2} = 1}$ of t…

math.PR2025

Strong Topological Trivialization of Multi-Species Spherical Spin Glasses

Brice Huang, Mark Sellke

We study the landscapes of multi-species spherical spin glasses. Our results determine the phase boundary for annealed trivialization of the number of critical points, and establis…

math.PR2025

Capacity threshold for the Ising perceptron

Brice Huang

We show that the capacity of the Ising perceptron is with high probability upper bounded by the constant $I^\pm_{⋆} \approx 0.833$ conjectured by Krauth and MÃ©zard, under the condi…

math.PR2024

Brice Huang, Sidhanth Mohanty, Amit Rajaraman +1

There has been a recent surge of powerful tools to show rapid mixing of Markov chains, via functional inequalities such as PoincarÃ© inequalities. In many situations, Markov chains…