Grégory Miermont

I'm a researcher at the Maths Laboratory of Paris-Sud University, and visiting Cambridge's Statistical Laboratory during this term. You can reach me at either of the following addresses:

gregory 'at' statslab 'dot' cam 'dot' ac 'dot' uk
Gregory 'dot' Miermont 'at' math 'dot' u-psud 'dot' fr

Advanced Probability

Here are the lecture notes and exercises — they are still subject to modifications and might not exactly match the contents of the lectures in places. Comments and corrections will be greatly appreciated!
Full text (with exercises).
Last modifications (besides obvious typos):

Setting in the beginning of Chapter 4 is slightly more detailed.
Minor modifications and add-ons around Proposition 4.1.1. More detailed proof.
Updated proof of Wiener's theorem, now matching this year's lecture. Slight changes around the statement of the reflection principle.

Example sheets will be displayed here progressively.
Example sheet '0' (There will be no supervision on these exercises — please ask me if you're having difficulties in solving them)
Example sheet 1. On conditional expectation and discrete-time martingales.
Example sheet 2. On martingale convergence theorems in discrete and continuous time.
Example sheet 3. On weak convergence and Brownian motion.
Example sheet 4. On Brownian motion and Poisson measures.

Some of the relevant books for this course are

R. Durrett. Probability: theory and examples. Second edition. Duxbury Press, Belmont, CA, 1996.
O. Kallenberg. Foundations of Modern Probability. Second edition. Probability and its Applications. Springer-Verlag, New York, 2002.
L. C. G. Rogers, D. Williams. Diffusions, Markov processes, and martingales. Vol. 1. Foundations. Reprint of the second (1994) edition. Cambridge Mathematical Library. Cambridge University Press, Cambridge, 2000.
D. W. Stroock. Probability theory, an analytic view. Cambridge University Press, Cambridge, 1993.
D. Williams. Probability with martingales. Cambridge Mathematical Textbooks. Cambridge University Press, Cambridge, 1991.

Link to my professional page in Paris-Sud.

Random Matrices and Enumeration of Maps

Informal reading group Past sessions:

Thursday 16 November. (Speaker: Stefan Großkinsky). After Ramirez, Rider and Virag,
Beta ensembles, stochastic Airy spectrum, and a diffusion, arXiv:math.PR/0607331.

Thursday 9 November. (Speaker: Ben Graham). Second presentation on Guionnet and Maurel-Segala's paper, or how matrix models relate to the Schwinger-Dyson equation.

Thursday 2 November. Schwinger-Dyson's equation and map enumeration, after Guionnet and Maurel-Segala
Combinatorial aspects of matrix models, arXiv math.PR/0503064.

Thursday 26 October. We showed how physicists are able to use the orthogonal polynomial method to obtain explicit formulas for generating functionals of maps of given genus (after Lando and Zvonkin).

Thursday 19 October. We discussed the link between the partition function of matrix models and enumeration of labelled diagrams. We saw how one can compute the partition function with the help of certain orthogonal polynomials. Taken after Lando and Zvonkin, Graphs on Surfaces and their Applications (Springer), Chapter 3.

Last modified: 24 November, 2006