From the 2 of 15 linked papers with an AI index.
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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…
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 in the regime $ β^2\mathrm{E}[ \mathrm{sech…
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…
Fluctuations in Quantum Unique Ergodicity at the Spectral Edge
Lucas Benigni, Nixia Chen, Patrick Lopatto +1
We study the eigenvector mass distribution of an Wigner matrix on a set of coordinates satisfying for some constant . For eigenvectors corresp…
Maximum gap in complex Ginibre matrices
Patrick Lopatto, Moritz Otto
We determine the asymptotic size of the largest gap between bulk eigenvalues in complex Ginibre matrices.