Mark Kac Seminar 2009-2010

December 4, 2009

11:15-13:00	speaker: Christina Toninelli (LPMA Paris)	title: A bootstrap-like algorithm with a discontinuous glass transition
	abstract: We introduce a stochastic lattice gas model with Glauber dynamics and kinetic constraints, the Spiral Model. We show the occurrence at a finite critical density of a transition displaying the unconventional properties of the liquid/glass transition. Above the critical density ergodicity is broken due to the appearance of an infinite spanning cluster of blocked particles whose density is discontinuous at the transition. Furthermore, the size of the blocked clusters diverges exponentially as the critical density is approached from below. We will explain how this transition is due to the occurrence of an unconventional percolation transition for a related bootstrap-like algorithm.
14:15-16:00	speaker: Vladas Sidoravicius (CWI / Leiden)	title: On non-uniqueness for specifications (g-functions or chains with infinite connections)
	abstract: The question of whether a specification, also referred as g-function or “chain with infinite connections”, uniquely determines the stationary process under natural “mixing” assumption, has been prominent since the pioneering work of Döblin and Fortet (1937). However in the past time reasonable progress was achieved only in providing sufficient conditions for the uniqueness of Gibbs measure. Bramson and Kalikow (1993) provided a remarkable, and for long time unique example of a continuous and regular specification that admits multiple Gibbs measures. During the talk I will review already known facts and will present a new non-uniqueness result, which in combination with uniqueness criteria of Johansson and Öberg (2003) determines the optimal modulus of continuity for a specification which admits multiple Gibbs measures.

Mark Kac Seminar 2009-2010

last updated: 22 sep 2009 by Markus