Cristian Giardinà - teaching activities

INFO for academic year 2009-2010

The course is in collaboration with Andreas Lopker.

Topics: renewal theory, martingales, random walk, Brownian motion.

Book: Stochastic Process (2nd edition) by S.M. Ross

We will post here problem sets, which are also handled during the lectures.
The solution of the problem sets is due for the following lecture (however they are not used in the evaluation).
See also the webpage of Andreas Lopker for exercises on renewal theory.

Syllabus 2009/2010

Problem set 1 (due October 13)
Problem set 2 (due October 20)
Problem set 3 (due November 12)
Problem set 4 (due December 1)
Problem set 5 (due December 10)
Problem set 6 (due December 17)

INFO past academic years

Syllabus 2008/09
Exam (with solutions) 15 January 2009 , 10 March 2009

Syllabus 2007/08
Exams: 25 January 2008 (solutions problems 2 and 4), 14 March 2008

Syllabus 2006/07
Exams: 29 January 2007 (solutions), 23 March 2007 (solutions problem 2)

INFO for academic year 2009-2010

The course will be self-study course (independent learning under supervision).
It will take place during Semester B Quartile 4. There will be a one-hour lecture
(see owinfo for the date) where the course content will be presented.

If you are interested, please make contact with responsible teachers:
C. Giardina' (HG 10.22) and F. Nardi (HG 10.20).

The subject of the course will be an introduction to Large Deviation theory, with application to Statistical Mechanics.

For the general part you can follow the book by F. Den Hollander.
You should be familiar with the content of Chapter 1 (Cramer's theorem for i.i.d. sequences), Chapter 2 (Sanov's
theorem for the empirical measure), Chapter 3 (Varadhan's lemma) , Chapter 5 (Gartner-Ellis theorem for
dependent sequences).
For the parte on application to Statistical Mechanics, material will be discussed later. You might start from the
following lectures notes: Lecture 1 , Lecture 2, Lecture 3.

EXAM:

• 50% of the final mark will be associated to the following problem sets.
  Problem set 1,
  Problem set 2,
  Problem set 3,
  Problem set 4,
  Problem set 5,
  Problem set 6.
  
  
• 50% of the final mark will be determined by an assignment. Work in pairs on a topic to be decided together
  with the responsible teacher. Examples:
  
  * Importance Sampling: understand the alghoritm and implement it in a MonteCarlo simulation.
  * Proof that the free energy of the Ising model in an infinite dimensional lattice coincide with the free energy
  of the mean-field Curie-Weiss model. Based on the study of a paper by Thompson.
  * Large deviation for random matrices (suggested by A. Fey).

INFO past academic years 2006-2007

The course was also held in 2006-2007, 2007-2008, 2008-2009.

Topics: probability theory, discrete and continous random variables, introduction to statistics.

Studyguide, Exams: 23 March 2007 (solutions), 11 May 2007 (solutions)