Paul Nikolaev
Dr. · Postdoctoral Researcher
TU Berlin
Research profile
Paul Nikolaev studies interacting particle systems and their continuum limits. His research addresses mean-field limits, common noise, fluctuations and large deviations, with links to nonlinear PDEs, stochastic control and optimal transport.
Research areas
Nonlinear PDEs · Stochastic Dynamics · Non-equilibrium Statistical Mechanics, Interacting Particle Systems and Fluctuating Hydrodynamics
Five research keywords
interacting particle systems · mean-field limits · common noise · Gaussian fluctuations · stochastic PDEs
Contact and links
Academic links
Curriculum vitae
| Date | Appointment / education |
|---|---|
| Current | Research Fellow, Stochastic Analysis in the Sciences, Technische Universität Berlin; funded by CRC/TRR 388 project A11. |
| 08.2025–01.2026 | Visiting Researcher, Columbia University, New York, USA. |
| 10.2024–07.2025 | Postdoctoral Researcher, University of Padova, Italy. |
| 09.2024 | PhD in Mathematics completed, University of Mannheim, Germany; thesis on mean-field limits for stochastic particle systems with and without common noise. |
Publications
This catalogue contains all publications by the member, including work from before joining SAiS. Journal versions and preprints are maintained as one record per scientific work.
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Convergence rate for Fluctuations of mean field interacting diffusion and application to 2D viscous Vortex model and Coulomb potential
For a system of mean field interacting diffusion on $\mathbb{T}^d$, the empirical measure $μ^N$ converges to the solution $μ$ of the Fokker-Planck equation. Refining this mean field limit as a Central Limit Theorem, the fluctuation process $ρ^N_t= \sqrt{N}( μ^N_t -μ_t)$ convergences to…
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Fluctuation behaviour for interacting particle systems with common noise
Published · Stochastics and Partial Differential Equations: Analysis and Computations (2026). We consider the asymptotic behaviour of the fluctuation process for large stochastic systems of interacting particles driven by both idiosyncratic and common noise with an interaction kernel \(k \in L^2(\R^d) \cap L^\infty(\R^d)\). Our analysis relies on uniform relative entropy estimates and Kolmogorov’s…
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Quantitative relative entropy estimates for interacting particle systems with common noise
Published · SIAM Journal on Mathematical Analysis 57(3), 3071–3109 (2025). We derive quantitative estimates proving the conditional propagation of chaos for large stochastic systems of interacting particles subject to both idiosyncratic and common noise. We obtain explicit bounds on the relative entropy…
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Characterization of Besov spaces with dominating mixed smoothness by differences
Published · Mathematische Nachrichten 298(7), 2116–2151 (2025). Besov spaces with dominating mixed smoothness, on the product of the real line and the torus as well as bounded domains, are studied. A characterization of these function spaces in terms of…
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Quantitative relative entropy estimates on the whole space for convolution interaction forces
Quantitative estimates are derived, on the whole space, for the relative entropy between the joint law of random interacting particles and the tensorized law at the limiting systeme. The developed method combines the relative entropy method under the moderated interaction…
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Well-posedness of diffusion-aggregation equations with bounded kernels and their mean-field approximations
Published · Mathematical Methods in the Applied Sciences 47(11), 9222–9248 (2024). The well-posedness and regularity properties of diffusion-aggregation equations, emerging from interacting particle systems, are established on the whole space for bounded interaction force kernels by utilizing a compactness convergence argument to treat…
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Hegselmann–Krause model with environmental noise
Published · Transactions of the American Mathematical Society 378(1) (2025). We study a continuous-time version of the Hegselmann-Krause model describing the opinion dynamics of interacting agents subject to random perturbations. Mathematically speaking, the opinion of agents is modelled by an interacting particle…
Current SAiS projects
CRC/TRR 388 project A11
Funded researcher working on interacting-particle fluctuations and stochastic dynamics.
Talks and posters
| Date | Talk / event |
|---|---|
| 08.2026 | Partial Differential Equations for Many Particles Systems, ICERM, Brown University. |
| 07.2026 | The 15th AIMS Conference, Athens. |
| 03.2026 | Stochastic Seminar, University of Vienna. |
| 10.2025 | IDEAS Seminar, The University of North Carolina at Chapel Hill. |
| 10.2025 | Stochastic and PDE Seminar, Georgia Tech. |
| 09.2025 | Seminar, Columbia University. |
| 04.2025 | Workshop on Regularisation by Noise, TU Wien. |
| 03.2025 | German Probability and Statistics Days, University of Dresden. |
| 02.2025 | Seminars in Probability and Finance, University of Padova. |
| 05.2024 | SPDEvent, University of Bielefeld. |
| 01.2024 | Seminar, Peking University. |
| 03.2023 | German Probability and Statistics Days, University of Essen. |
| 11.2022 | Workshop on Recent Advances in Non-local Kinetic, Fluid and Diffusive PDEs, Liaoning University. |
| 09.2022 | SPDEvent, University of Bielefeld. |
| 08.2022 | 17th Doctoral Meeting in Stochastics, University of Klagenfurt. |
Teaching
| Term | Teaching activity |
|---|---|
| Spring 2024 | Teaching Assistant: Dynamical Systems; Teaching Assistant: Stochastic Analysis. |
| Autumn 2023 | Teaching Assistant: Mean-field particle systems and their limits to non-local PDEs. |
| Spring 2023 | Teaching Assistant: Advanced Topics in Mathematical Finance; Teaching Assistant: Stochastic Analysis. |
| Autumn 2022 | Head Teaching Assistant: Analysis 1. |