Decay of Correlations for the Hardcore Model in Random Regular Graphs
Tuesday, March 17, 2015 - 4:00pm - 4:40pm
Klaus 2443
Nayantara Bhatnagar (University of Delaware)
Gibbs measures on trees play a central role in the theory of spins systems on random graphs. We determine the local weak limit of the hardcore model on random regular graphs upto a density for the largest independent set that is bounded by and goes asymptotically to the condensation threshold. We show that the hardcore measure converges in probability locally in a strong sense to the free boundary condition Gibbs measure on the tree. As a consequence, the reconstruction threshold on the random graph is equal to the reconstruction threshold on the d-regular tree. We expect that our methods should generalize to a wide range of spin systems for which the second moment method holds.
This is joint work with Allan Sly and Prasad Tetali.
This is joint work with Allan Sly and Prasad Tetali.