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From the 2 of 13 linked papers with an AI index.

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13 papers

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 loss. Assuming only known bounds on…

math.PR2026

Full replica symmetry breaking in the Sherrington-Kirkpatrick model

Patrick Lopatto

The paper proves that for the Sherrington‑Kirkpatrick spin glass at zero external field and any inverse temperature β>1, the Parisi measure is supported on a single interval with a…

math.ST2026

On Rates Attainable under Random Design: A Negative Answer to a Problem of Robins

P. M. Aronow, Patrick Lopatto

The paper proves that in nonparametric regression with random design, the conjectured optimal convergence rate for estimating a constant conditional variance is unattainable, estab…

math.PR2026

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…

math.ST2026

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…

math.PR2026

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 in the regime $ β^2\mathrm{E}[ \mathrm{sech…