## PhD course in probability (Lecturer: Erik Broman)

#### spring 2015

**Latest update:**

27/4: Posted solution to HA2. All assignments have been corrected and can
be found in my mailbox.
**Schedule:**

A link to the schedule:

https://se.timeedit.net/web/uu/db1/schema/ri157XQQ589Z50Qf57083gZ6y6Y7809Q5Y41Y0.html
or even better, go here, and search for my name.
Observe that this schedule will likely change, so make sure you check back regularly.

**Home assignments:**

Home assignment 1 can be found
here. The solution can be found
here.
Home assignment 2 can be found
here. The solution can be found
here.

**Some pictures:**

The first picture
shows how we go from site-percolation on the triangular lattice, and end up with
a percolation model on the faces of the hexagonal lattice.
The second picture shows
a box in the hexagonal lattice.

**Further information:**

For more information (including a short overview of the topics we will cover) and planning of lectures, please go
here. Again, please observe that this will
be updated and adjusted during the course, so make sure that you check back regularly.

**Exam**

Home assignments. They will be posted here as they are given.

**Purpose of course**

To gain basic knowledge of 'modern' probability theory.

**Literature:**

**For measure and Integration Theory:**

D. Williams: Probability with martingales, Cambridge Mathematical Textbooks
Cambridge University Press, Cambridge, 1991. ISBN: 0-521-40455-X; 0-521-40605-6

G. B. Folland: Real Analysis, Modern Techniques and Their Applications

**For convergence:**

R. Durrett: Probability:Theory and Examples

G. Grimmett and D. Stirzaker: Probability and Random Processes

P. Billingsley: Convergence of Probability Measures

**For ordinary percolation:**

G Grimmett: Percolation

B. Bollobas and O. Riordan: Percolation