onderwijs
Random networks for communication
In this course, we will discuss material from the book Random Networks for Communication, by Franceschetti and Meester. You can download a pdf file of the book by clicking here. We will discuss most of Chapter 1-3 and a few things from Chapter 6 (see also below under ‘Schedule’).
!!!From September 12 on, we will
always start at 9.15!!!
Exam
There is a take-home exam at the end of the course. You find the exam of two years ago here, this should give some impression about what you can expect.
Schedule
During the course, I will post the things we have done here, and will try to predict as much as I can what we will do the coming few weeks. Roughly speaking, I plan to do (in that order) 2.2, 2.3, 3.1, 3.2, 1.2, 2.5, 2.7, 3.3, parts of 6.3, but this may change during the course.
September 5: Material: general introduction; Theorem 2.2.2 and Theorem 2.2.5. Exercises: 2.4; 2.5; Read Definition 2.2.3 and Theorem 2.2.4 and give a proof of this last theorem.
September 12: Material: finish 2.2; start with 2.3. Exercises: 2.1-2.3; 2.6.
September 19: Material: finish 2.3; Proposition 3.2.5; Theorem 3.1.3. Exercises: Show that d_TV(X(n),X) -> 0 if and only if X(n) converges to X in distribution (see page 70 below Definition 3.1.2); 2.16.
October 3: Material: finish 3.2; start with 1.2. Exercises: Find the correct scaling for full connectivity on a 2n x n rectangle. In the lectures, we did this for an n x n square, and on a rectangle it will be a little bit different. Try to figure this out.
October 10: Material: finish 1.2; discuss all previous exercises; start with 2.4. Exercises: 16, 17 below.
October 17: Material: finish 2.4. Exercises: 2.10; Can you find a concrete number k such the k-th nearest neighbour model in two dimensions is supercritical?
October 31: Material: 2.1 (to be studied at home – I will not discuss this in class); 2.5 until Theorem 2.5.2 (inclusive). Exercises: 2.7, 2.8, 2.9.
November 7: Material: start 2.7. Exercises: 2.12, 2.13.
November 14: Material: finish 2.7 (that is, until 2.7.3 inclusive). Exercises: Exercise 6 of the exam two years ago, 2.18, 2.19, 2.20, 2.14.
November 21: Material: 3.3 until beginning of 3.3.2.
November 28: Material: Finish 3.3.
December 5: Material: 3.4.
December 12: Material: 6.3.1.