P. M. Aronow

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math.PR2026

Quantitative Parisi formulas and fluctuations in the Sherrington-Kirkpatrick model

P. M. Aronow, Patrick Lopatto

We establish quantitative Parisi formulas and fluctuation bounds for the Sherrington-Kirkpatrick model at zero external field. In particular, using that the Parisi measure is suppo…

math.PR2026

Optimal central limit theorem for bounded random variables in high dimensions

P. M. Aronow, Patrick Lopatto

Let $W = n^{- 1/2} \sum_{i = 1}^{n} X_{i}$ , where the $X_{i}$ are independent centered random vectors in $R^{p}$ with $∣ X_{ij} ∣ \leq B$ almost surely. Suppose that $Cov (W)$ has un…

math.PR2026

Replica symmetry breaking at arbitrary depth

P. M. Aronow, Patrick Lopatto

We study finite-step replica symmetry breaking (RSB) in mixed even $p$ -spin Ising spin glasses at positive temperature and zero external field. For every integer $k \geq 1$ , we const…