UVictoria Probability and Dynamics Seminar: Peter Eichelsbacher

In the talk exchangeability appears in two different meanings. In the first part, the determination of the phase diagram of the Curie-Weiss model relies on De Finetti’s Theorem. The Curie-Weiss distribution will be expressed as a random mixture of Bernoulli distributions. The competition between the Gaussian randomness in the CLT of Bernoulli’s and the randomness in their mixture replaces the standard energy-entropy competition. In the second part, we study a mean-field spin model with three- and two-body interactions. In a recent paper by Contucci, Mingione and Osabutey, the equilibrium measure for large volumes was shown to have three pure states, two with opposite magnetization and an unpolarized one with zero magnetization, merging at the critical point.

The aim is to apply the exchangeable pair approach due to Stein to prove (non-uniform) Berry-Esseen bounds, a concentration inequality, Cramér-type moderate deviations and a moderate deviations principle for the suitably rescaled magnetization.