Universität Duisburg-Essen
Fachbereich Mathematik
Anton Klimovsky und Anita Winter

23th March 2016

Master Seminar (2SWS)
Summer Semester 2016
Tuesday, 14.15-15.45; WSC-S-U-3.02

Master Seminar: Branching Brownian motion

Branching Brownian motion (BBM) is a popular probabilistic model for spatial branching. It combines two classical models: Brownian motion (totally random motion) and the Galton-Watson (GW) process (totally random genealogy). BBM is a natural spatial embedding of the GW process: Each GW particle gets a position in space and wanders randomly and independently around after its birth. In this seminar, we will especially be interested in the behaviour of the extremal particles (i.e., those having largest/smallest positions) of BBM as time progresses.

Tentative Schedule:

  1. 12.04.; Introduction in the topic and organization of the presentations
  2. 03.05. Introduction in branching processes und Branching Brownian motion, Anita Winter
  3. 10.05. F-KPP equation,
  4. 24.05. Derivative martingale + extreme value theory, Anton Klimovsky
  5. 31.05. Feynman-Kac representation + The maximum principle and its applications I, Tim Kalkmann
  6. 07.06. The maximum principle and its applications II, Erik Wellner
  7. 14.06. Estimates on solutions of the linear F-KPP equation + Brownian bridges, Severin Matthes (Josten)
  8. 21.06. Hitting probabilities of curves, Qianli Ma
  9. 28.06. Asymptotics of solutions, Geronimo
  10. 05.06. Convergence result,
  11. 12.07. The extremal process of BBM,

Literature:

  • Anton Bovier, Branching Brownian motion, lecture notes, 2015. pdf

  • What should I know if I want to participate?
    The Seminar is offered as part of the Master Program in Mathematics. Nevertheless, if you are interested in probability theory you are very welcome to participate and contribute with a presentation. Preknowledge are the course Probability Theory II (Wahrscheinlichkeitsthoerie II). Don't hesitate to send me an e-mail for more information:

    anita(dot)winter `at' due(dot)de

    The first session will be on Tuesday, 12th of April. Anton Klimovsky will give a short introduction and we will distribute the talks. The first presentation will be given on Tuesday, 26th of April.