Percolation, Fall 2014


General

This page gives some General Information on the course, and each week I will indicate here which material has been treated.



Literature used

We use parts of the book `Probability on Graphs' by Geoffrey Grimmett (Cambridge University Press 2010), as well as lecture notes (which will be updated/extended regularly: see below in the section `Material treated') and some literature available from the internet.


Homework assignments

Three times a set of Homework exercises will be given (and posted on this page, in the section `Material treated' below). For each set, the students have one week to make the exercises. Working on homework in pairs is encouraged. The average of the three homework grades contributes twenty percent to the final grade.


Exam

On Thursday December 11 a take-home exam was given.

The re-examination (a WRITTEN EXAM) will take place on Thursday January 29, 14:00 - 17:00, in room M129 at the VU (in the same building where the lectures took place).

It is allowed to bring the lecture material treated at the course. It is NOT allowed to use a calculator or other electronic equipment.

As to the computation of the final grade after this re-examination: The average homework grade will only be taken into account (for twenty percent) if this is favourable.


Material treated

Here I will mark each week which material I have treated.

week 37: Informal introduction/overview, and Grimmett, Section 3.1.

week 38: LECTURE NOTES (until, but not including, Theorem 2.10). Here are the ILLUSTRATIONS 1-5 for these notes.

week 39: Section 3 of LECTURE NOTES. Here are the corresponding ILLUSTRATIONS 6-10.

week 40: Section 4 of LECTURE NOTES. Here is the FIRST SET OF HOMEWORK EXERCISES. Note that there are FOUR(!) Exercises. Deadline is 10 a.m. on Monday October 13.

week 41: Section 5 of LECTURE NOTES. (Typo in equation (23) corrected).

week 42: Grimmett, Section 5.3. Homework solutions presented and discussed by Rene Conijn.

week 43: Grimmett, Section 5.7 up to (and including) the proof of Lemma 5.53.

week 44: Grimmett, Section 5.7 `almost' completed (except page 120).

week 45: Grimmett Section 5.7 completed; started introduction to hulls and capacities (notes will be provided next week). Here is the SECOND SET OF HOMEWORK EXERCISES.

week 46: The material treated this week corresponds with part of the lecture notes (by F. Camia) of which I distributed hard copies in class: Section 5 and the beginning of Section 6. (In week 45 the contents of Section 4 of these notes was treated).

week 47: Section 1 of LECTURE NOTES on introduction to SLE. Solutions of Homework 2 were presented by Rene Conijn. Here is the THIRD SET OF HOMEWORK EXERCISES (WITH CORRECTED VERSION OF EXERCISE 3).

week 48: Section 2 of LECTURE NOTES on introduction to SLE.

week 49: Explained how one-arm probabilities in `the scaling limit' imply one-arm exponents for the discrete percolation model. Homework 3 solutions were discussed by Rene Conijn.


Last updates: January 22, 2015