Bálint Tóth:

PERCOLATION (BMETE955303)

Spring 2015

 

Taught course of the Graduate Schools of Mathematics of BME, ELTE and CEU

 

Lectures: Thursday 10:15-12:00 am (first lecture: 12 Feb 2015)

Requirements for BME students / Követelmények BME hallgatóknak (in Hungarian)

Syllabus (sketchy)

LECTURE NOTES (downloadable handwritten lecture notes)

1.   Introduction, definitions, basics (Hammersley, Harris ineq., stochastic domination)

2.   p>pc: uniqueness of the infinite cluster in Z^d (Aizenman-Kesten-Newman, Burton-Keane); continuity of p→θ(p) (van den Berg-Keane) 

3.   Further tools: (1) van den Berg-Kesten inequality; (2) Russo’s formula

4.   Sharpness of the phase transition (Menshikov, Aizenman-Barsky, DuminilCopin-Tassion)

5.   Two dimensions 1: Planar duality and its consequences, Sykes-Essam, Harris-Kesten-Russo

6.   Two dimensions 2: Russo-Seymour Welsh Theorem and its first consequesnces

7.   Two dimensions 3: Conformal invariance of 2d critical percolation: Cardy’s Formula, Smirnov’s Theorem

8.   Stochastic Löwner Evolution (SLE): Introduction, basics

 

FURTHER READING

Research  papers

                Books

 

EXAM