Events/Conferences

Current:

Conference at the University of Münster (9-13 September 2024): Probability, Dynamics and the Geometry of Groups

Past:

Conference at the University of Münster (20-24 June 2022): Quantum Many Body Systems and Interacting Particles: In honor of Herbert Spohn

Conference at the University of Münster (26-30 August, 2019): Dynamics, Random Media and Universality of Complex Physical Systems

Conference at Weierstrass Institute/ TU Berlin (15-19 August, 2016): Conference celebrating the 75th birthday of S.R.S.Varadhan

 Teaching

Publications and Preprints

• Randomized Geodesic Flow on Hyperbolic Groups (joint work with Luzie Kupffer and Mahan Mj), arxiv: 2411.14350

• Coarse Embeddability, L^1-Compression and Percolations on General Graphs (joint work with Konstantin Recke), arxiv: 2406.04222

• Self-Repellent Brownian Bridges in an Interacting Bose Gas (joint work with Erwin Bolthausen and Wolfgang König), arxiv: 2405.08753

• Additive-Multiplicative Stochastic Heat Equations, Stationary Solutions, and Cauchy Statistics (joint work with Alex Dunlap), arxiv: 2402.02907

• Effective Mass of the Fröhlich Polaron and the Landau-Pekar-Spohn Conjecture (joint work with Rodrigo Bazaes, Mark Sellke and S.R.S. Varadhan), arxiv: 2307.13058

• Haagerup Property and Group-Invariant Percolation (joint work with Konstantin Recke), arXiv: 2303.17429

• Positive and Negative Moments for Directed Polymers in Eandom environment in Weak Disorder (joint work with Rodrigo Bazaes), arXiv: 2212.06029

• Schur Multipliers of C^*-algebras, Group-Invariant Compactification and Applications to Amenability and Percolation (joint work with Konstantin Recke), arXiv: 2211.11411, (to appear in Journal of Functional Analysis)

• Subcritical Gaussian Multiplicative Chaos in the Wiener Space: Construction, Moments and Volume Decay (joint work with Rodrigo Bazaes and Isabel Lammers), arxiv: 2211.08996, (to appear in Probability Theory and Related Fields)
• Stochastic Homogenization for Hamilton-Jacobi-Bellman Equations on Continuum Percolation Clusters (joint work with Rodrigo Bazaes and Alexander Mielke), arxiv: 2208.07269
• The Effect of Disorder on Quenched and Averaged Large Deviations for Random Walks in Random Environments: Boundary Behavior. (joint work with Rodrigo Bazaes, Alejandro Ramírez and Santiago Saglietti), Stochastic Processes and Applications, 158, 208-237 (2023))  arxiv: 2101.04606
• Geometry of the Gaussian Multiplicative Chaos in the Wiener Space (joint work with Yannic Bröker), arxiv: 2008.04290
• Commutative Diagram of the Gross-Pitaevskii Approximation. (joint work with Stefan Adams), arxiv: 1911.09635
• On Null-homology and Stationary Sequences. (joint work with Gerold Alsmeyer), Journal of Theoretical Probability, 36, 2476-2500 (2023)),  arxiv: 1910.07378
• Quenched and Averaged Large Deviation Rate Functions for Random Walks in Random Environments: the Impact of Disorder (joint work with Rodrigo Bazaes, Alejandro Ramírez and Santiago Saglietti), (Annals of Applied Probability, 33 (3), 2210-2246 (2023))  arxiv: 1906.05328
• Space-time fluctuation of the Kardar-Parisi-Zhang equation in d≥3 and the Gaussian free field. (joint work with Francis Comets and Clément Cosco), (Ann IHP. Probability and Statistics, 60(1), 82–112 (2024))  arxiv: 1905.03200
• Renormalizing the Kardar–Parisi–Zhang Equation in 𝑑≥3 in Weak Disorder. (joint work with Francis Comets and Clément Cosco). Journal of Statistical Physics volume 179, pages 713–728 (2020), arxiv: 1902.04104
• Identification of the Polaron Measure in Strong Coupling and the Pekar variational Formula. (joint work with S.R.S. Varadhan). Annals of Probability, Vol. 48 (5), 2020, pp 2119-2144, arxiv: 1812.06927
• Localization of the Gaussian Multiplicative Chaos in the Wiener Space and the Stochastic Heat Equation in Strong Disorder. (joint work with Yannic Bröker). Annals of Applied Probability, Vol. 29 (6), 2019, pp 3745-3785, arxiv: 1808.05202
• Fluctuation and Rate of Convergence for the Stochastic Heat Equation in Weak Disorder (join work with Francis Comets and Clement Cosco), arxiv: 1807.03902
• Strong Coupling Limit of the Polaron measure and the Pekar Process. (joint work with S.R.S. Varadhan), arxiv: 1806.06865
• Corrigendum and addendum: Identification of the Polaron Measure I: Fixed Coupling Regime and the Central Limit Theorems for Large Times. (joint work with S.R.S. Varadhan).  Communications on Pure and Appled Mathematics, Vol. 75(2), 2022, pp 1642-1653 (proof of Theorem 4.5 in arXiv: 1802.05696)
• Identification of the Polaron Measure I: Fixed Coupling Regime and the Central Limit Theorem for Large Times. (joint work with S.R.S. Varadhan).  Communications on Pure and Applied Mathematics, Vol. 73 (2), 2020, 350-383, arxiv: 1802.05696
• Quenched Central Limit Theorem for the Stochastic Heat Equation in Weak Disorder, (join work with Yannic Bröker), (Springer: Probability and Analysis in Interacting Physical Systems, in honour of S. R. S. Varadhan), arxiv: 1710.00631
• Central Limit Theorem for Gibbs Measures on Path Spaces Including Long Range and Singular Interactions and Homogenization of the Stochastic Heat Equation. Annals of Applied Probability, Vol. 32 (3): 2028-2062 (2022) arxiv: 1706.09345
• Quenched Large Deviations for Simple Random Walks on Percolation Clusters Including Long-Range Correlations. (join work with Noam Berger and Kazuki Okamura). Communications in Mathematical Physics, Vol. 358, 2018, pp 633–673, arxiv: 1612.01393
• Weak and Strong Disorder for the Stochastic Heat Equation and Continuous Directed Polymers in d≥3. (join work with A. Shamov and Ofer Zeitouni). Electronic Communications in Probability, Vol. 21, 2016, pp 1-12, arxiv: 1601.01652
• Mean‐Field Interaction of Brownian Occupation Measures II: A Rigorous Construction of the Pekar Process. (join work with Erwin Bolthausen and Wolfgang König), Communications on Pure and Applied Mathematics, Vol. 70 (8), 2017, pp 1598-1629, arxiv: 1511.05921
• Gibbs Measures on Mutually Interacting Brownian Paths under Singularities. Communications on Pure and Applied Mathematics, Vol. 70 (12), 2017, pp 2366-2404, arxiv: 1510.04663
• Mean-Field Interaction of Brownian Occupation Measures, I: Uniform Tube Property of the Coulomb Functional (joint work with Wolfgang König), Ann. IHP, Probability and Statistics, 53:4, 2214-2228 (2017), arxiv: 1509.06672
• Quenched Large Deviations for Simple Random Walks on Supercritical Percolation Clusters (joint work with Noam Berger), arxiv: 1501.02730
• Brownian Occupation Measures, Compactness and Large Deviations (joint work with S.R.S. Varadhan), Annals of Probability, 44:6, 3934-3964 (2016), arxiv: 1404.5259
• Large Deviations for Brownian Intersection Measures (joint work with Wolfgang König), Communications on Pure and Applied Mathematics, 66:2, 263-306 (2013), arxiv: 1105.1063

Supervision of bachelor and master theses

Supervised master theses:

- Luzie Kupffer, Universität Münster, Wintersemester 2021 (Topic: Tightness of Liouville first passage percolation)

-Carolin Dobbelhoff, Universität Münster, Wintersemester 2021 (Topic: Approximation des Maximalen Schnitts und Erkennung von Communities)

- Isabel Lammers, Universität Münster, Sommersemester 2021 (Thema: Electrical networks and asymptotic behavior of random walks on graphs)

- Nadine Woltering, Universität Münster, Sommersemester 2021 (Topic: Coupling techniques and Markov chains)

-Konstantin Recke, Universität Münster, Wintersemester 2020-2021 (Topic: Percolation on non-amenable groups and hyperbolic plane)

- Binan Gu, Courant Institute of Mathemetical Sciences, New York University, Spring semester 2016 (Topic: Critical branching random walks in a random environment)

Supervised bachelor theses:

- Matthias Fechner, Universität Münster, Summer semester 2024

- Lennart Noske, Universität Münster, Summer semester 2024

- Jannik Schlatt, Universität Münster, Summer semester 2024

- Carolin Dobbelhoff, Universität Münster, Sommersemester 2019 (Thema: Spektrales Clustering und die Cheeger Ungleichung)

- Konstantin Recke, Universität Münster, Sommersemester 2019 (Topic: Wigner's semicircle law and free probability)

- Alicia Schuller, Universität Münster, Sommersemester 2019 (Thema: Betrügererkennung mit Deep Learning)

- Anna Moshkova, Universität Münster, Sommersemester 2020 (Thema: Das Johnson-Lindenstrauss Lemma und Gordons Theorem)

- Johannes Altrock, Universität Münster, Sommersemester 20 (Thema: Community detection und Stochastic Block Model)

- Lukas Endeman, Universität Münster, Sommersemester 2020 (Topic: Diffusion maps & Isomap: Applications to Nonlinear Dimensionality Reduction and Semi-supervised Learning)