Probability reading group

The probability reading group provides a chance to learn about an area of probability at a post-graduate level, and will also let participants practice presenting maths to a small audience. More detailed information will appear here soon!

For further information please contact paw at warwick dot ac dot uk.

Current topic

Topics previously covered

Spring 2018 (Wednesdays 11-12 in room C1.06) -- Random processes with reinforcement

Some references:
A survey of random processes with reinforcement (Robin Pemantle) : https://arxiv.org/pdf/math/0610076.pdf
Edge-reinforced random walk, vertex-reinforced jump process and the supersymmetric hyperbolic sigma model (Christophe Sabot and Pierre Tarres) : https://arxiv.org/pdf/1111.3991.pdf

Fall 2017 (Mondays 15-16 in room C0.08) -- First-passage percolation

Main reference:
50 years of first passage percolation (Antonio Auffinger, Michael Damron, Jack Hanson) : https://arxiv.org/abs/1511.03262

Spring 2017 (Thursdays 12-1 pm in room B3.01) -- Random Maps.

Main reference:

Aspects of Random Maps (Grégory Miermont). Preprint on the webpage of the author:
http://perso.ens-lyon.fr/gregory.miermont/coursSaint-Flour.pdf

Fall 2016 (Thursdays 10-11 in room B1.01) -- Random Interlacements.

Main references:

An Introduction to Random Interlacements (Drewitz, Rath, Sapozhnikov); [Link to Springer version]

Vacant set of random interlacements and percolation (Sznitman).

Spring 2016 - The Loop-Soup Model

Main reference:

Loop Measures and the Gaussian Free Field. G. F. Lawler and J. Perlman.

Autumn 2015 - Percolation and Unimodularity.

Main reference:

Percolation on Trees and Networks. R. Lyons and Y. Peres.

Spring and Summer 2014 - Random walks

Main references:

Principles of Random Walk. F. Spitzer.

Random walks on graphs. M. T. Barlow.

Markov chains and mixing times. D. A. Levin, Y. Peres, E. L. Wilmer.

Spring 2013 - Gaussian Processes and local times

Main reference:

Markov Processes, Gaussian Processes and local times. M. B. Marcus, J. Rosen.

Autumn 2012 - Gaussian processess

Main reference:
Gaussian processes. T. Hida, M. Hitsuda.

Autumn 2011 and Spring 2012 - Probability on graphs

Main reference:
Probability on graphs. G. R. Grimmett.

Summer 2011 - Local times

Main reference:
Continuous martingales and Brownian motion. D. Revuz, M. Yor.

Autumn 2010 and Spring 2011 - Lévy processes

Main references:
Lévy processes. J. Bertoin.

Lévy processes and stochastic calculus. D. Applebaum.

Questions from our sessions appear here: Sheet 1, Sheet 2, Sheet 3.

Autumn 2009 and Spring 2010 - Fluctuation theory for Lévy processes

Main reference:
Introductory lectures on fluctuations of Lévy processes with applications. A. Kyprianou.

Summer 2009 - Optimal stopping

Main reference:

Optimal stopping and free-boundary problems. G. Peskir, A. Shiryaev.

Autumn 2008 and Spring 2009 - Large deviations

Main references:

Large deviations. F. den Hollander.

Large deviations techniques and applications. A. Dembo, O. Zeitouni.

Large deviations. J.-D. Deuschel, D. W. Stroock

Spring 2008 - Analytic inequalities and random walks on graphs

Main references:

Characterization of sub-Gaussian heat kernel estimates on strongly recurrent graphs. M. T. Barlow, T. Coulhon, T. Kumagai.

Parabolic Harnack inequality and estimates of Markov chains on graphs. T. Delmotte.

Harnack inequalities and sub-Gaussian estimates for random walks. A. Grigor'yan, A. Telcs.

Autumn 2007 - Fragmentation and coagulation.

Main reference:

Random fragmentation and coagulation processes. J. Bertoin.

Summer 2007 - Random walks in a random environment.

Main reference:

Random walks in random environment. O. Zeitouni.

Spring 2007 - Schramm-Loewner evolution.

Main references:

Conformally invariant processes in the plane. G. F. Lawler.
Random planar curves and Schramm-Loewner evolution. W. Werner.

Autumn 2006 - The concentration of measure phenomenon.

Main reference:
The concentration of measure phenomenon. M. Ledoux.

paw@warwick.ac.uk