6 papers · 1 filter
Mixing of Glauber Dynamics on High Overlap Gibbs Measures
Afonso S. Bandeira, Ahmed El Alaoui, Almut Rödder
We show fast mixing of Glauber dynamics for certain quadratic Gibbs measures with large external fields. The main ingredient is an overlap condition that allows us to control corre…
Hardness of sampling solutions from the Symmetric Binary Perceptron
Ahmed El Alaoui, David Gamarnik
We show that two related classes of algorithms, stable algorithms and Boolean circuits with bounded depth, cannot produce an approximate sample from the uniform measure over the se…
On the Discontinuous Breaking of Replica Symmetry and Shattering in Mean-Field Spin Glasses
Antonio Auffinger, Ahmed El Alaoui, Mark Sellke
We show that in mean-field spin glasses, a discontinuous breaking of replica symmetry at the critical inverse temperature implies the existence of an intermediate shattered…
Near-optimal shattering in the Ising pure p-spin and rarity of solutions returned by stable algorithms
Ahmed El Alaoui
We show that in the Ising pure -spin model of spin glasses, shattering takes place at all inverse temperatures when is sufficie…
Fast relaxation of the random field Ising dynamics
Ahmed El Alaoui, Ronen Eldan, Reza Gheissari +1
We study the convergence properties of Glauber dynamics for the random field Ising model (RFIM) with ferromagnetic interactions on finite domains of , . Of p…
Bounds on the covariance matrix of the Sherrington-Kirkpatrick model
Ahmed El Alaoui, Jason Gaitonde
We consider the Sherrington-Kirkpatrick model with no external field and inverse temperature and prove that the expected operator norm of the covariance matrix of the Gibbs…