Mark Kac Seminar 2009-2010

April 9, 2010

11:15-13:00	speaker: Yvan Velenik (Genève)	title: A finite-volume version of the Aizenman-Higuchi theorem for the 2d Ising model
	abstract: In the early 1980s, in two celebrated papers, Aizenman and Higuchi independently established that all infinite-volume Gibbs states of the two-dimensional ferromagnetic nearest-neighbour Ising model are convex combinations of the two pure phases mu^+ and mu^-. I'll present a new approach to this result, based on the Ornstein-Zernike theory. This approach presents a number of advantages: (i) we obtain a finite-volume, quantitative analogue (implying the classical, infinite-volume claim); (ii) the scheme of our proof seems more natural and provides a clear picture of the underlying phenomenon; (iii) this new approach seems substantially more robust. This is joint work with Loren Coquille. Additional material: Please find here the slides of Velenik's first and second lecture.
14:15-16:00	speaker: Nicolas Pétrélis (Nantes)	title: A polymer in a multi interface medium
	abstract: We consider a model for an homopolymer interacting with an infinity of interfaces. The polymer configurations (after n steps) are given by the trajectories of a n-step directed simple random walk in dimension 1+1. The medium consists in an infinity of equi-spaced horizontal interfaces and we allow the distance (T) between two consecutive interfaces to grow with the size of the polymer (n). The interaction between the polymer and these interfaces takes the form of an homogeneous pinning or depinning term. We discuss in particular the vertical speed at which the right extremity (Sn) of the polymer travels in the medium. More precisely, we display the scaling limit of (Sn) for every interaction intensity and every growth regime of Tn.

Mark Kac Seminar 2009-2010

last updated: 02 mar 2010 by Markus