Introduction to percolation theory (or, why statistical physicists make life difficult for themselves)
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).
This is a roughly weekly series of didactical blackboard talks focussing on some theoretical aspect of Condensed Matter, Biological, and Statistical Physics..