Tel Aviv University - Horowitz Seminar Dear all, The fall semester at Tel Aviv University begins next week and the Horowitz seminar on Probability, Ergodic Theory and Dynamical Systems renews its activity. As in previous years we will meet each week on Mondays from 14:30 to 15:30 in room 309 of Schreiber building, unless otherwise announced. Please send email to me if you wish to join or leave the mailing list. This week we are happy to have: Speaker: Yinon Spinka, Tel Aviv University Title: The Random Graph-Homomorphism Model Date: Monday, October 22 Time: 14:30 Place: Schreiber 309 Abstract: We discuss the random graph-homomorphism model introduced by Benjamini, Häggström and Mossel (2000). This model generalizes the simple random walk on Z, and therefore, is sometimes referred to as a G-indexed random walk or a random height function on a graph. We begin by introducing the model (no prior knowledge is assumed) and by giving some examples. We then give a short survey of known results and discuss some conjectures. The main questions of interest are the variance at a given vertex and the range a of random homomorphism. We then continue on to our results. We study two certain families of graphs (which can be seen as modifications of a torus or a line segment) and show a sharp transition in the behavior of a typical homomorphism. The main results will be stated and outlines and ideas of some proofs will be given. This work answers a question posed by Benjamini, Yadin and Yehudayoff (2007). Have a good semester! Ron Seminar webpage: <http://www.math.tau.ac.il/~peledron/Horowitz_seminar/Horowitz_seminar.html> --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Ron Peled <peledron@post.tau.ac.il>