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.





References:

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