Pierre Nolin: Catalogue data in Autumn Semester 2016
|Name||Dr. Pierre Nolin|
Professur für Mathematik
ETH Zürich, HG G 37.2
|401-3604-66L||Special Topics in Probability: Recent Developments in Percolation Theory||4 credits||2V||P. Nolin|
|Abstract||The goal of this course is to present recent developments in Percolation Theory|
|Objective||The goal of this course is to present recent developments in Percolation Theory|
|Content||Independent percolation is obtained by deleting randomly (and independently) the edges of a lattice, each with a given probability p between 0 and 1. One is then interested in the connectivity properties of the random subgraph so-obtained. It is arguably the simplest model from statistical mechanics that displays a phase transition, a drastic change of behavior as the parameter p varies.|
We will first present classical tools and properties of percolation theory: in particular correlation inequalities, exponential decay of connection probabilities, and uniqueness of the infinite connected component. We will then discuss recent developments: for example percolation on Cayley graphs, and continuum limits in two dimensions.
|Literature||B. Bollobas, O. Riordan: Percolation, CUP 2006|
G. Grimmett: Percolation 2ed, Springer 1999
|Prerequisites / Notice||Prerequisites:|
401-2604-00L Probability and Statistics (mandatory)
401-3601-00L Probability Theory (recommended)
|401-4600-66L||Student Seminar in Probability |
Limited number of participants.
Registration to the seminar will only be effective once confirmed by email from the organizers.
|4 credits||2S||A.‑S. Sznitman, J. Bertoin, P. Nolin, W. Werner|
|Content||The seminar is centered around a topic in probability theory which changes each semester.|
|Prerequisites / Notice||The student seminar in probability is held at times at the undergraduate level (typically during the spring term) and at times at the graduate level (typically during the autumn term). The themes vary each semester.|
The number of participants to the seminar is limited. Registration to the seminar will only be effective once confirmed by email from the organizers.
|401-5600-00L||Seminar on Stochastic Processes||0 credits||1K||J. Bertoin, A. Nikeghbali, P. Nolin, B. D. Schlein, A.‑S. Sznitman, W. Werner|