P. M. Aronow

collaborators

8 papers

cs.LG2026

A positive resolution of the gap-entropy conjecture

P. M. Aronow, Nathan Kallus, Patrick Lopatto

We prove the gap-entropy conjecture for fixed-confidence best-arm identification with independent unit-variance Gaussian arms, means in $[0, 1]$ , and a unique optimal arm. For each…

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…

math.ST2026

Adaptive Confidence Sets for Binary Regression without Design Smoothness

P. M. Aronow, Patrick Lopatto

We study honest adaptive confidence sets for the regression function in random-design binary regression under $L^{2} (d x)$ loss. Assuming only known bounds $0 < c \leq g \leq C < \infty$ on…

math.ST2026

Nearly-minimax variance estimation under rough random design

P. M. Aronow, Patrick Lopatto

We identify the minimax exponent for constant conditional variance estimation under rough random design. The unknown design density is bounded above and away from zero, with no smo…