9 papers · 1 filter
Fast mixing in Ising models with a negative spectral outlier via Gaussian approximation
Dan Mikulincer, Youngtak Sohn
We study the mixing time of Glauber dynamics for Ising models in which the interaction matrix contains a single negative spectral outlier. This class includes the anti-ferromagneti…
Balanced multi-species spin glasses
Erik Bates, Youngtak Sohn
We identify a special class of multi-species spin glass models: ones in which the species proportions serve to ''balance'' out the interaction strengths. For this class, we prove a…
Free energy in multi-species mixed -spin spherical models
Erik Bates, Youngtak Sohn
We prove a Parisi formula for the limiting free energy of multi-species spherical spin glasses with mixed -spin interactions. The upper bound involves a Guerra-style interpolati…
Replica symmetry breaking in multi-species Sherrington-Kirkpatrick model
Erik Bates, Leila Sloman, Youngtak Sohn
In the Sherrington-Kirkpatrick (SK) and related mixed -spin models, there is interest in understanding replica symmetry breaking at low temperatures. For this reason, the so-cal…
Stochastic block models with many communities and the Kesten--Stigum bound
Byron Chin, Elchanan Mossel, Youngtak Sohn +1
We study the inference of communities in stochastic block models with a growing number of communities. For block models with vertices and a fixed number of communities , it…
Rapid phase ordering for Ising and Potts dynamics on random regular graphs
Reza Gheissari, Allan Sly, Youngtak Sohn
We consider the Ising, and more generally, -state Potts Glauber dynamics on random -regular graphs on vertices at low temperatures . The mixin…