- Series
- Stochastics Seminar
- Time
- Tuesday, March 1, 2011 - 4:05pm for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Robert Ziff – Michigan Center for Theoretical Physics, Department of Chemical Engineering, University of Michigan
- Organizer
- Yuri Bakhtin
Various exact results in two-dimensional percolation are presented.
A method for finding exact thresholds for a wide variety of systems,
which greatly expands previously known exactly solvable systems to
such new lattices as "martini" and generalized "bowtie" lattices, is given.
The size distribution is written in a Zipf's-law form in terms of the enclosed-
area distribution, and the coefficient can be written in terms of the
the number of hulls crossing a cylinder. Additional properties of hull
walks (equivalent to some kinds of trajectories) are given. Finally,
some ratios of correlation functions are shown to be universal, with
a functional form that can be found exactly from conformal field theory.