**Undergraduate Seminar: Percolation Theory**

Tuesday nights in Math 507 at 7pm.

Organized by Alice Rizzardo, office in Math 408.

Official instructor: Daniela De Silva (please refer to her for bureaucratic matters).

If you are not registered please register. If you would like to be part of my section please email me if you haven't.

See this expository article to get a first idea of what percolation is and for nice pictures.

This java applet lets you play with site percolation.

Kherani and Bagchi, lecture notes from this course.

Meester, Lecture notes in percolation

Steif, A mini course on percolation therory

Grossglauser, Thiran, Networks out of control

Bollobas and Riordan, Percolation, Cambridge University Press.

Grimmet, Percolation, Springer.

Tsitsiklis, Fundamentals of probability, notes here http://stellar.mit.edu/S/course/15/fa11/15.085/materials.html

Calendar

Week
Day
Topic
Speaker
References
Week 1
January 23
Overview. Fundamentals of probability
Daniel
K&B lecture 1; Tsitsiklis; B&R
Week 2
January 31
Solutions to the exercises
Matt
Borel-Cantelli lemma. Kolmogorov's 0-1 law
Jessie
K&B lecture 1; Tsitsiklis; B&R
Week 3
February 7
Percolation on a tree. Existence of critical probability for percolation on Z^2
Monica
B&R pp.5-11, K&B lecture 2
Harris' lemma and applications
Sidney
B&R pp.37-43, K&B lecture 3
Week 4
February 14
BK inequality and applications
Jon
B&R pp. 42-44, K&B lecture 4 for applications
Margulis-Russo lemma
Yiren
B&R pp. 46-47
Week 5
February 21
Duality
Jason
B&R pp. 50-57
Harris's Theorem
Kaz
B&R, 3.1-3.2
Week 6
February 28
Subcritical phase: exponential decay of the cluster radius I
Will
Grimmet, 5.1-5.2
Subcritical phase: exponential decay of the cluster radius II
Matt
Grimmet, 5.1-5.2
Week 7
March 20
Subcritical phase: exponential decay of the cluster radius III
Kaz
Grimmet, 5.1-5.2
Exponential decay of the cluster size distribution
Sidney
K&B Lecture 7
Week 8
March 27
The infinite cluster is unique
Will
K&B Lecture 9
Exponential decay of the radius of an infinite open cluster, I
Yiren
K&B Lecture 10
Week 9
April 3
Exponential decay of the radius of an infinite open cluster, II
Jason
K&B Lecture 10
The critical probability for bond percolation on a 2-dimensional lattice is 1/2
Jessie
Grimmett, pp.287-295
Week 9
April 10
Real-world applications
Monica