Teaching
Seminar: Large Deviations (SoSe20)
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.
Literature:
- Frank den Hollander. Large Deviations. American Mathematical Soc., 2008.
Useful links:
Course: Probability Theory II (WS19/20)
(Wahrscheinlichkeitstheorie II)
Research
Submitted papers/Preprints
- 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.
Published/Accepted papers
- 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
- YEP XV "Information Diffusion on Random Networks"
Eindhoven, Netherlands - APPROX/RANDOM 2018
Princeton, USA - Strongly Correlated Random Interacting Processes
Oberwolfach, Germany
Mini CV
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.