22 citations · 30 across the 31 of their papers we have counts for
14 papers · 1 filter
Overlap structure of mixed even -spin models
P. M. Aronow, Patrick Lopatto
We identify the limiting overlap structure of mixed even -spin models, including the Sherrington-Kirkpatrick model, at every fixed deterministic external field. In particular, w…
Parisi measure of the Sherrington-Kirkpatrick model with external field
Patrick Lopatto
We prove that the Parisi measure of the Sherrington-Kirkpatrick model has connected support at every positive temperature and every positive external field. When the model breaks r…
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 , and a unique optimal arm. For each…
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…
Optimal central limit theorem for bounded random variables in high dimensions
P. M. Aronow, Patrick Lopatto
Let , where the are independent centered random vectors in with almost surely. Suppose that has un…
Replica symmetry breaking at arbitrary depth
P. M. Aronow, Patrick Lopatto
We study finite-step replica symmetry breaking (RSB) in mixed -spin Ising spin glasses at positive temperature and zero external field. For every integer , we construct…
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 loss. Assuming only known bounds on…
Full replica symmetry breaking in the Sherrington-Kirkpatrick model
Patrick Lopatto
We prove that, at zero external field and for every inverse temperature , the Parisi measure of the Sherrington-Kirkpatrick model is supported on an interval , with a…
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…
Sobolev convergence of log-determinants for smooth Wigner matrices
Giorgio Cipolloni, Patrick Lopatto
We show that the fields emerging from the log-determinant and the eigenvalue counting function of smooth Wigner matrices converge in law to centered Gaussian, logarithmically corre…
Minimax unbiased estimation for finite populations with bounded outcomes
P. M. Aronow, Patrick Lopatto
We study design-unbiased estimation of the finite-population total when each outcome satisfies known bounds . For any sampling design with inclu…
Replica symmetry up to the de Almeida-Thouless line in the Sherrington-Kirkpatrick model
Patrick Lopatto
We show that in the Sherrington-Kirkpatrick model at inverse temperature with uniform external field , replica symmetry holds for the set of pairs predicted by de…
One-step TMLE for weighted average treatment effects
Yang Liu, Patrick Lopatto, Ivana Malenica
We consider Targeted Maximum Likelihood Estimation (TMLE) of weighted average treatment effects (WATEs), a class of causal estimands that reweight the covariate distribution using…
Mobility Edge for the Anderson Model on Random Regular Graphs
Suhan Liu, Patrick Lopatto
We determine the phase diagram of the Anderson tight-binding model on random regular graphs with Gaussian disorder and sufficiently large degree. In particular, we prove that if th…