**Teaching**

Information about regular courses can be found on** blackboard**.

**Regular courses are**

**1. Bachelor Level **

**Inleiding Kansrekening (WI1614)**

**Statistiek (WI3104TN)**

**2. Master Level **

**Martingales, Brownian motion and stochastic processes (WI4330)**

**Mathematical Methods for nano-science: NB4010 (in collaboration with Dr. J.L.A. Dubbeldam) **

**Optional Master Course: Interacting particle systems: Theory and Applications.**

**Will not be taught in 2015-2016, will be taught again in 2016-2017.**

Interacting particle systems are a class of Markov processes with many (possibly infinitely many) interacting components.

They are useful in the modelling of several real-world phenomena in physics, biology and economy.

Phenomena modeled by interacting particle systems are the** spread of an infection** (contact process), the **evolution of opinions** in a population (voter model). Interesting, macrosopic changes in behavior can occur as a function of the parameters in the model: these relate to phase transitions and percolation. E.g in the virus spread model the phase transition is between survival or extinction of the infection started from a single infected individual, in the opinion model between coexistence of different opinions or ``freezing'' (i.e. eventually only states with full consensus remain). In models of statistical physics the emergence of **spontaneous magnetization** is modelled, as well as phenomena such as **nucleation or metastability** (e.g. supercooled droplets). They are also used to model** non-equilibrium systems**, such as systems in contact with two different temperatures: the stationary state of such a system is carries a current from the hot to the cold reservoir, and has a highly non-trivial correlation structure.In economics, interacting particle are used to model e.g. the **dynamics of distribution of wealth.**

Interacting particle systems known under the name ``Glauber and Kawasaki dynamics'' are also very useful in Markov Monte Carlo methods to sample from a Gibbs distribution.

In the course we give the** basic mathematical techniques used in this field:** Markov semigroups and generators, invariant measures, ergodicity, coupling, monotonicity, duality. We illustrate these techniques in the context of the symmetric and asymmetric exclusion process. This model is used in statistical physics as well as in the theory of traffic flow.

Lecture notes of Liggett are available here.