Research Interests
As a researcher, I am interested in various areas of probability, particularly in the behavior of stochastic processes under constraints. This is a classic field, which can be traced back at least to Doob's work in the 1950s. It plays an important role both in theory and in applications. Currently, I am mainly working on conditioning various types of stochastic processes on rare events, including:
- Brownian motion and related Markov processes,
- branching Brownian motions,
- stationary Gaussian processes.
Further, I am concerned with probabilistic foundations of machine learning, focussing on reinforcement learning. Yet another project deals with the limiting behavior of heavy-tailed quadratic chaos.
Publications
- Brownian Motion Conditioned to Have Restricted L_2-norm.
Ann. Inst. Henri Poincaré Probab. Stat., to appear. arXiv:2312.12982 [math.PR].
joint work with Frank Aurzada and Mikhail Lifshits - Brownian Motion Conditioned to Spend Limited Time Outside a Bounded Interval -- An Extreme Example of Entropic Repulsion.
Bernoulli 31(2): 1428-1450, 2025.
joint work with Frank Aurzada and Martin Kolb - Brownian Motion with Limited Occupation Times.
Doctoral thesis, Technical University of Darmstadt, 2024. - Brownian Motion Conditioned to Spend Limited Time Below a Barrier.
Stochastic Process. Appl., 146:360-381, 2022.
joint work with Frank Aurzada
Talks and Conferences
- 07/2025: invited talk - Probability Colloquium (Munich, Germany)
- 07/2025: organization of a contributed session and talk - 44th Conference on Stochastic Processes and their Applications (Wroclaw, Poland)
- 06/2025: talk - Research Seminar in Probability Theory (Paderborn, Germany)
- 05/2025: Rossfest70 celebrating 70 years of Ross Pinsky (St. Louis, USA)
- 03/2025: contributed talk - Spring School on Extrema of Log-Correlated Random Fields (Darmstadt, Germany)
- 03/2025: contributed talk - German Probability and Statistics Days 2025 (Dresden, Germany)
- 02/2025: Workshop on Reinforcement Learning (Mannheim, Germany)
- 08/2024: invited talk - Conference on Stochastic Processes Under Constraints (Bielefeld, Germany)
- 08/2024: contributed talk - Bernoulli-IMS 11th World Congress in Probability and Statistics (Bochum, Germany)
- 08/2024: poster - BS-IMS World Congress Pre-Meeting for Young Researchers 2024 (Essen, Germany)
- 04/2024: invited talk - Research Seminar in Probability Theory (Paderborn, Germany)
- 02/2024: contributed talk - Spring School on Multiplicative Chaos and Cascade (Darmstadt, Germany)
- 01/2024: invited talk - Research Seminar in Probability Theory (Munich, Germany)
- 12/2023: invited talk - National Seminar on Probability and Statistics (Sofia, Bulgaria)
- 11/2023: talk - What is ...? Seminar in preparation of the Mathematical Colloquium (Darmstadt, Germany)
- 07/2023: poster - 43rd Conference on Stochastic Processes and their Applications (Lisbon, Portugal)
- 03/2023: Spring School on Probabilistic Methods in Population Biology (Darmstadt, Germany)
- 02/2023: contributed talk - German Probability and Statistics Days 2023 (Essen, Germany).
- 11/2022: invited talk - Research Seminar in Stochastics (Augsburg, Germany)
- 07/2022: 10th International Conference on Lévy Processes (Mannheim, Germany)
- 03/2022: contributed talk - Spring School on Random Geometric Graphs (Darmstadt, Germany)
- 03/2022: Conference on Branching and Persistence (Saumur, France)
- 01/2022: talk - What is ...? Seminar in preparation of the Mathematical Colloquium (Darmstadt, Germany)
- 10/2021: invited talk - National Seminar on Probability and Statistics (Sofia, Bulgaria)
- 09/2021: contributed talk - German Probability and Statistics Days 2021 (Mannheim, Germany)
- 07/2021: 15th PhD Students' Conference in Stochastics (Munich, Germany)
- 04/2021: invited talk - Research Seminar in Probability Theory (Paderborn, Germany).
- 09/2020: Workshop on Stochastic Processes under Constraints (Oberwolfach, Germany)
- 03/2020: Spring School on Complex Networks (Darmstadt, Germany)
- 02/2019: contributed talk - Spring School on Selected Topics in Stochastic Geometry (Darmstadt, Germany)
- 10/2018: talk - Research Seminar in Stochastics (Darmstadt, Germany)