Konstantin Matveev
Subtitle:
2D phenomena in Probability
Course Description:
This topics course will focus on two-dimensional phenomena in Probability coming mostly from statistical physics, including tilings, vertex models, percolation, Schramm–Loewner evolution, etc.
Prerequisites:
16:642:591 or permission of the instructor
Text:
Several sources
Schedule of Sections:
Previous Semesters:
- Notes on lectures 1 and 2 up to conditional expectation.
- Notes on the Dunford-Pettis compactness criterion
- Note: Exercise 5 of lecture 1 was misstated. For the correct statement and an extension of the problem, see the lecture 1 notes. I posted a corrected version on Feb. 6.
- Notes on lectures 2,3, and 4 on discrete-time martinagles.
- Notes on the definition of Brownian motion
- (Lecture Notes 4) Further notes on constructing Brownian motion
- (Lecture Notes 5) Notes on Levy processes
- (Lecture Notes 6) Filtrations and stopping times in continuous time; Applications to Levy processes
- (Lecture Notes 7) Introduction to Stochastic Integration