Topics Course: Combinatorial Stochastic Processes, Summer 2016


Lectures: Wednesday 12-2PM, Friday 2-4PM, Endenicher Allee 60, SemR 0.007

Instructor: Ngoc Tran (office 4.034, HCM building, Endenicher Allee 60)

Prerequisites: graduate probability

Books and resources: Pitman, Combinatorial stochastic processes; Bertoin, Random fragmentation and coagulation processes.

Course setup: 4 hours of lectures per week

Class project: Contribution to the CSP update project

Final exam: The final exam will be 30 minutes long, on the course content.

Course description : Topics covered include random partitions, random trees, branching processes, fragmentation and coalescent. The lecture notes are largely based on various texts and papers on these topics, especially the two books `Combinatorial Stochastic Processes' (Pitman), `Random fragmentation and coagulation processes' (Bertoin).
This course is part of an ongoing effort to update Jim (Pitman)'s textbook and the status of the open problems in that text. Therefore, students are strongly encouraged to contribute by updating the status of one open problem in Pitman's textbook. (See Class Project)


Syllabus

  1. Random exchangeable partition
  2. Random combinatorial trees and forests
  3. Exchangeable fragmentation
  4. Exchangeable coalescent
  5. Real trees and the standard additive coalescent

Course materials:

Lecture notes: last updated: June 12, 2016
Lecture notes June (1), hand-written
Lecture notes June (2), hand-written
Lecture notes June (3), hand-written
Lecture notes July (1), hand-written
Lecture notes July (2), hand-written
Lecture notes July (3), hand-written
Papers of interest
Ballot Theorem: Old and New

Exam dates

First round: July 27, 28, 29.
Second round: September 29, 30.

Exam topics

Exam topics