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
      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
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,
Seminar webpage:
Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <> 
Announcement from: Ron Peled   <>