Lorenzo Bertini ( Univ . La Sapienza ,

S OF TALKS: Márton Balázs (University of Wisconsin): Construction of the zero range process and a deposition model with superlinear growth rates (Joint work with Firas Rassoul-Agha and Timo Seppäläinen) Construction of the zero range process and some related deposition processes is available following the methods initiated by T. M. Liggett and F. Spitzer, and E. D. Andjel. These methods work under the assumption that the jump rates of the process are either bounded, or at least are of bounded increments as functions of the local configuration. However, recent results involving stationary shock measures shed light on processes with jump rates depending exponentially on the local configuration. The methods mentioned above do not seem to extend for constructing the dynamics of such a process. The talk will sketch estimates based on probabilistic coupling arguments, which make a construction possible in the case of (at most) exponentially growing jump rates. Unfortunately, difficulties arising due to the fast-growing rates only allowed us to establish parts of the usual Markov-semigroup machinery. Gérard Ben Arous (NYU Courant Institute): Title to be announced Abstract not available.not available. Jacob van den Berg (CWI Amsterdam): Conditional correlation inequalities in static and dynamic contexts (Joint work with J. Kahn and O. Haggstrom) Consider ordinary bond percolation on a finite or countably infinite graph. Let s, t, a and b be vertices. In a paper with Kahn (2001) it has been shown that, conditioned on the event that there is no open path from s to t, the two events “there is an open path from s to a” and “there is an open path from s to b” are positively correlated. In recent papers with Haggstrom and Kahn this result has been extensively generalized, with applications to contact processes. Preservation (in a temporal as well as in spatial sense) has also been investigated. A dual version of our results gave a proof of a conjecture of N. Konno for the 1D contact process. In this talk I will explain these results and discuss relations with results by Belitsky, Ferrari, Konno and Liggett (1997), Liggett and Steif (2004) and Liggett (2005).