EVENT DETAILS AND ABSTRACT

Title: Random Current Representation of the Ising Model and its Application to Gaussianity in High Dimensions, Part I
Speaker: Hugo Duminil-Copin
Speaker Info: Institut des Hautes Etudes Scientifiques
Brief Description:
Special Note:
Abstract:

The talk will discuss the Ising model random current representation. This classical representation enables to rewrite spin and energy correlations via systems of random currents with prescribed sources. One may then interpret the deviation from Wick's law in terms of intersection probabilities of random currents. This was used in a recent proof that in four dimensions the spin fluctuations of Ising-type models at their critical points are Gaussian in their scaling limits (infinite volume, vanishing lattice spacing). Other results can be derived via this representation and we will review some of them (Joint work with Michael Aizenman.)