- Vivi Padova
- Il Bo
Wednesday 29 October 2008 h. 15:00, room 2BC/30
Marco Formentin (Ph.D. in Applied Math., Dip. Mat.)
"Information Flow on Trees: the Reconstruction Problem and the Purity of the Free Gibbs Measure"
The Reconstruction Problem on a tree can be stated as follows. We send a signal from the root to the boundary, making a prescribed error at every edge of the tree. Suppose you know what happens at distance N from the origin of the tree. What can you say about the original signal sent from the root when N goes to infinity? This problem, concerning the flow of information on trees is equivalent to the purity of the free Gibbs Measure for the Ising/Potts models on a tree. Purity can be regarded as a special kind of phase transition. We review this equivalence and give old and new thresholds for the transition to purity for the free Potts Gibbs measure on regular trees.
Rif. int. C. Marastoni, T. Vargiolu, M. Dalla Riva