The seminal result in probability is the central limit theorem, a tool that tells us how ever larger sums of random variables fluctuate around their mean. A natural question that one might pose at this stage is: how can we describe events where this sum deviates from its mean by more than a “normal’’ amount? Answering this questions plays a crucial role in many fields such as probability theory, statistics, financial mathematics, operations research, ergodic theory, information theory, statistical physics and many more. In this seminar we will look at large deviation theory, by first looking at a toy example of sums of i.i.d. random variables. Once the basic concepts are understood, we will present the result in a more abstract/general way and look at a few more tailored statements.
- Frank den Hollander. Large Deviations. American Mathematical Soc., 2008.
The lecture is a natural continuation of the course Probability Theory I. It is aimed at Masters students doing a degree in mathematics or economathematics and belongs to the area of stochastic and insurance mathematics.
The lecture will be held in English.
ExaminationsOral examinations will take place in Room 118 of the Mathematical insitute and be scheduled on a case per case basis. Please register for an examination slot by sending me an email at least a week ahead of time.
- Achim Klenke. Probability theory: A comprehensive course. Universitext. Springer, London, second edition, 2014.
- Rick Durrett. Probability: theory and examples. Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press, Cambridge, fourth edition, 2010.
- R. M. Dudley. Real analysis and probability, volume 74 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge, 2002. Revised reprint of the 1989 original.
- Daniel W. Stroock. Probability theory: An analytic view. Cambridge University Press, Cambridge, second edition, 2011.
Other useful links:
- Percolation phase transition in weight-dependent random connection models
with Lukas Lüchtrath and Peter Mörters, arXiv:2003.04040.
- Recurrence versus Transience for Weight-Dependent Random Connection Models
with Markus Heydenreich, Christian Mönch and Peter Mörters, arXiv:1911.04350.
- The age-dependent random connection model with Arne Grauer, Lukas Lüchtrath and Peter Mörters, Queueing Syst (2019)
- Percolation of Lipschitz surface and tight bounds on the spread of information among mobile agents with Alexandre Stauffer, APPROX-RANDOM 2018: 39:1-39:17
- Multi-scale Lipschitz percolation of increasing events for Poisson random walks
with Alexandre Stauffer, Annals of Applied Probability, 29 (2019), 376-433
- Random walks in random conductances: decoupling and spread of infection
with Alexandre Stauffer, Stochastic Processes and their Applications, 129 (2019) 3547
Recent conferences/workshops where I have given a talk
Since this is supposed to be a sort of CV website, I should probably list a couple of things that define me. In no specific order, here's a few things I have done.