Ben Gurion University
Department of Mathematics
Percolation
Course: 201.2.0101 Spring 2013
Overview
The course is intended for anyone with a basic course in probability.
This course concerns the physical notion of phase transition,
specifically in the model known as "percolation".
We will review the main mathematical results regarding percolation
and its related counterparts the Ising model, Potts model and FortuinKasteleyn cluster model,
starting from works of Ising and Peierls in the beginning of the 20th century and
culminating in modern work of Smirnov.
The topics in the course are, time permitting:
 Percolation on graphs. Definitions and basic properties
 Harris' inequality
 van den BergKesten inequality, Reimer's inequality
 Russo's formula
 BurtonKeane Theorem (AizenmanKestenNewman)
 Exponential decay of correlations in subcritical regime
 Planar percolation: RussoSeymourWelsh theory
 Planar percolation: the HarrisKesten theorem
 Conformal invariance: CardySmirnov formula on the triangular lattice
 Percolation on groups
 Critical percolation on nonamenable groups: BLPS
 Percolation on finite graphs: The ErdosRenyi model
Recommended Literature:

B. Bollobas and O. Riordan.
Percolation.
 G. Grimmett.
Percolation.
 R. Lyons with Y. Peres.
Probability on Trees and Networks.
 Hugo DuminilCopin's
Lecture Notes
(in French).


Lecture Notes
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(More lectures will be added.)