Probability and Stochastic Analysis - University of Bonn
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Graduate Seminar on Probability Theory, WS 2009/2010

Time, roomThursday, 14-16, LWK 1.008
StartFirst week of the semester
SupervisionPatrik Ferrari (LWK 347)

Subject

Seminar on Interacting particle systems

The main part will be based on T. Liggett's book Interacting Particle Systems:

Chapter 1.1,1.2: Markov processes, their semigroups and generators
Chapter 1.3: Construction of generators for particle systems
Chapter 1.4: Applications of the construction
Chapter 2.1,2.2: Coupling, monotonicity and positive correlations
Chapter 2.3,2.5: Duality and reversibility
Chapter 3: Applications of couplings and duality to spin systems

Depending on the numbers of participants one might also use the Lecture notes on probability theory, Springer Lecture Notes in Mathematics 1608 by R. Durrett.

For an example of interacting particle systems, see this Animation.