Title: Mean field Ising models
Authors: Sumit Mukherjee - Columbia University (United States) [presenting]
Anirban Basak - International Centre for Theoretical Sciences (India)
Nabarun Deb - Columbia University (United States)
Promit Ghosal - Columbia University (United States)
Abstract: The asymptotics of the log partition function of an Ising model on a sequence of finite but growing graphs/matrices are considered. We give a sufficient condition for the mean field prediction to the log partition function to be asymptotically tight, which in particular covers all graphs with average degree going to infinity. We show via several examples that our condition is ``almost necessary'' as well. As application of this mean field approach, we are able to do the following: a) Derive the asymptotics of the log partition function, b) Study consistency properties of the pseudo likelihood estimator, c) Study non degenerate limit distribution for the sum of spins.