Tel Aviv University This week at the Horowitz seminar on Probability, Ergodic Theory and Dynamical Systems at Tel Aviv University we are happy to have Dan Romik from UC Davis. Dan will also give a related talk at the Mathematics colloquium earlier this Monday, see <http://www.math.tau.ac.il/~ostrover/colloquium/colloq2012.html> but the Horowitz seminar talk will be self-contained. Speaker: Dan Romik, University of California, Davis Title: Loop percolation, pipe percolation and random noncrossing matchings Date: Monday, March 18 Time: 14:30 Place: Schreiber 309 Abstract: The talk will be about the same family of random noncrossing matchings introduced in my colloquium talk earlier on the same day, but the discussion will be self-contained and no previous knowledge will be assumed. My goal will be to show that these random noncrossing matchings appear as the connectivity patterns associated with a second (and seemingly unrelated) type of percolation called "pipe percolation". Pipe percolation was previously defined only on a cylindrical geometry (or equivalently as a discrete-time random walk on the finite set of generators of the Temperley-Lieb algebra), but extending the definition to the setting of the entire plane brings up new and subtle issues. I will define the process rigorously as a continuous-time Markov process taking values in the space of noncrossing matchings of the integers. The proof that the construction works will use ideas from ergodic theory and the theory of interacting particle systems. I will also discuss bounds on the matching distance, which relate to the well-known open problem of the "5/48" percolation critical exponent. Best regards, 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>