Probability seminar: Random Walks in a Random Environment (BM)
Collegejaar:  20172018 

Studiegidsnummer:  4373PRBSE 
Docent(en): 

Voertaal:  Engels 
Blackboard:  Onbekend 
EC:  6 
Niveau:  400 
Periode:  Semester 1 
 Wel Keuzevak
 Wel Contractonderwijs
 Wel Exchange
 Wel Study Abroad
 Geen Avondonderwijs
 Wel AlaCarte en Aanschuifonderwijs
 Geen Honours Class
Description
The probability seminar aims at exposing students to advanced probability theory and selected applications. One topic will be selected each year. The topic for the academic year 20172018 is Random Walks in Random Environments (RWRE).
RWRE are random walks on lattices with random transition probabilities, models for motion of particles through highly irregular media due to defects, impurities or fluctuations. Fundamental examples of Markov processes with random transitions, they were introduced in the 1970s motivated by some problems in biology, crystallography and metal physics, but later applications have spread through numerous areas. They represents a very active and challenging research area in probability and physics of disordered systems.
The focus of this course is on key wellunderstood models and related techniques which can be useful in other fields. The principal model to be discussed is a random walk with nearestneighbor jumps in independent identically distributed random environment on the one dimension lattice. Despite being the simplest model it shows a surprisingly reach behavior. Extensions and generalizations will be touched and a view of the state of the art in this area will be given.
Prerequisits
Familiarity with basic concepts in probability theory and basics of Markov chains and random walks.
Literature
The course material is based on the following key references together with selected topical research papers
which will be given during the course:
* O. Zeitouni, Random Walks in Random Environment, Lectures on Probability Theory and Statistics,
Ecole dEte' de Probabilite's de SaintFlour XXXI  2001, Lecture Notes in Mathematics, Volume 1837,
Part II, (2004).
Available version at the authorâ€™s webpage
* J. Peterson, Lecture Notes on Random Walks in Random Environments, (2013). Available at the
webpage of the author: webpage.
* F. den Hollander, Large Deviations, Fields Institute Monographs, vol. 14.S, (2000).
Plan and exam
Four introductory lectures plus another one at an advanced stage of the course are given by Avena and
den Hollander.
All the other lectures are given by the participants. Each participant gives 2 presentations:
* one dedicated to some aspects of the general theory,
* one chosen from the list of topics presented during the course.
For the second presentation, a short handout (to be distributed to the other participants) must be prepared
as well.
The final grade is based on active participation, the two presentations and the handout.
Maakt deel uit van  Soort opleiding  Semester  Blok 

Mathematics  Master  1  
Wiskunde  Bachelor  1 