6 papers
The free energy limit of the SYK model at high temperature
David Gamarnik, Francisco Pernice, Alexander Schmidhuber +1
The Sachdev-Ye-Kitaev (SYK) model is a disordered quantum mean-field model studied in condensed matter physics and the holographic theory of black holes. Its structural properties…
The Random Subsequence Model and Uniform Codes for the Deletion Channel
Ryan Jeong, Francisco Pernice
We introduce the Random Subsequence Model, a spin glass model on pairs of random strings whose partition function counts subsequence embeddin…
Rigorous Asymptotics for First-Order Algorithms Through the Dynamical Cavity Method
Yatin Dandi, David Gamarnik, Francisco Pernice +1
Dynamical Mean Field Theory (DMFT) provides an asymptotic description of the dynamics of macroscopic observables in certain disordered systems. Originally pioneered in the context…
Sequential Dynamics in Ising Spin Glasses
Yatin Dandi, David Gamarnik, Francisco Pernice +1
We present the first exact asymptotic characterization of sequential dynamics for a broad class of local update algorithms on the Sherrington-Kirkpatrick (SK) model with Ising spin…
The Fundamental Limits of Recovering Planted Subgraphs
Daniel Lee, Francisco Pernice, Amit Rajaraman +1
Given an arbitrary subgraph and , the planted subgraph model is defined as follows. A statistician observes the union a random copy of , together…
Counterexamples to a Weitz-Style Reduction for Multispin Systems
Kuikui Liu, Nitya Mani, Francisco Pernice
In a seminal paper, Weitz showed that for two-state spin systems, such as the Ising and hardcore models from statistical physics, correlation decay on trees implies correlation dec…