22 citations · 30 across the 31 of their papers we have counts for
9 papers · 2 filters
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…
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…
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…
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…
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…
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…