************************************ Tel Aviv University Hello everyone, The next colloquium talk will be held on: Monday, 14/01/2013, 12:15, Schreiber 006, Tel Aviv University. Speaker: Ofer Zeitouni (Weizmann Institute) Title: From KPP equations to the maxima of Gaussian free fields The abstract is given below. Tea and coffee at 12:00, same room. Hope to see you there. For information about future colloquia, see <http://www.math.tau.ac.il/~ostrover/colloquium/colloq2012.html> Yours, Yaron ************************************* Abstract: The Fisher-Kolmogorov-Petrovsky-Piscounov equation describes the propagation of a self interacting wave such as in flame propagation. Probabilistically, for appropriate initial conditions it describes the evolution of the location of the maximal particle in a system of branching random walks (where the total population size increases exponentially). That particle system was analyzed by Bramson using a mixture of probabilistic and analytic methods in the early 80's. In particular, the ``front'' of the propagating wave is delayed (by a logarithmic factor) behind the stationary, linear speed propagation. The Gaussian free field is a random Gaussian field that is indexed by points in $R^d$; in the critical dimension d=2, it represents a random distribution. A discrete analogue of the GFF can be defined on any finite graph. Of special interest are properties of the maxima of the field, and in particular the fluctuations of the maximum. After describing a general point of view that allows one to analyze branching particle systems, I will describe newly observed phase transitions that occur in the case of time-inhomogeneous media. I will then describe recent work that links the two objects, branching random walks and Gaussian free fields, in the critical dimension $d=2$. In particular, I will explain how Bramson's work can be adapted in order to show that the maximum of the two dimensional (discrete) GFF has fluctuations which are of order $1$. The talk is based on joint works with Maury Bramson, with Jian Ding and with Ming Fang. --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: <ostrover@post.tau.ac.il>