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### A Quenched Central Limit Theorem in the Annealed Region of the Viana-Bray Model

**Mathematical Physics & Probability**

Speaker: | Shannon Star, University of Rochester |

Location: | 2112 MSB |

Start time: | Wed, Mar 11 2009, 4:10PM |

In two elegant papers, Sourav Chatterjee and then Chatterjee and Nick Crawford applied Stein's method to the Sherrington-Kirkpatrick mean-field spin glass. Among other results, they proved a quenched CLT for the internal energy, at high temperature and also in the presence of an external magnetic field. With Brigitta Vermesi, we attempted to extend their results to the Viana-Bray diluted spin glass model in the annealed region delineated by Guerra and Toninelli (at high temperature and zero magnetic field). Roughly speaking, the Viana-Bray model is obtained from the SK model by replacing the Gaussian couplings by more general infinitely-divisible couplings. The main tool in the extension is the well-known theorem of L.H.Y. Chen extending Charles Stein's method to infinitely divisible distributions, which also generalizes Wick's rule.