Percolation is Odd
Cris Moore (Santa Fe Institute)
Abstract: In site percolation, a spanning configuration is a set of vertices that includes a path from the top of a lattice to the bottom. We prove that for square lattices of any height and width, the number of spanning configurations with an odd or even number of vertices differs by ±1. In particular, the total number of spanning configurations is always odd. (You may enjoy working out the proof on your own before the talk!) This result holds also for the hypercubic lattice in any dimension, with a wide variety of boundary conditions.
This is joint work with Stephan Mertens.
statistical mechanicsdiscrete mathematicscombinatoricsprobability
Audience: researchers in the discipline
LA Combinatorics and Complexity Seminar
Series comments: Password is on the seminar page. www.math.ucla.edu/~pak/seminars/CCSem-Fall-2020.htm
Organizers: | Igor Pak*, Greta Panova |
*contact for this listing |