Introduction to percolation theory (or, why statistical physicists make life difficult for themselves)

Statistical Physics and Complexity Group meeting

Introduction to percolation theory (or, why statistical physicists make life difficult for themselves)

  • Event time: All day
  • Event date: 12th October 2016
  • Speaker: (School of Physics & Astronomy, University of Edinburgh)
  • Location: Room 2511,

Event details

Consider a lump of Swiss cheese. Can you navigate from one side of the
cheese to the other through the holes? This is the fundamental question
that is asked in percolation theory. A simple model for the arrangement
of the holes has a nontrivial phase transition as the density of holes
is varied. Below the critical point, the probability of being able to
traverse an infinite system is zero; above the critical point, it is
nonzero. There are critical phenomena (power laws in various quantities)
at the percolation transition, characterised by a set of universal
critical exponents. We will obtain estimates of these critical exponents
by fair means and foul. If time permits, I will also briefly introduce
directed percolation, which has recently acquired a paradigmatic status
as a simple model for turbulence (but I shall defer to Alexander on that).