Highlights

Fluctuations in Continuum: conference at TU Berlin, 19–23 April 2027

Byadmin 9 October 2026

Our group is organizing Fluctuations in Continuum — Singular SPDEs, Stochastic Fluid Dynamics, and Nonequilibrium Statistical Mechanics, taking place at TU Berlin from 19 to 23 April 2027.

The conference brings together researchers working on stochastic partial differential equations, stochastic fluid dynamics, and nonequilibrium statistical mechanics. It aims to connect methods for singular SPDEs in critical and supercritical regimes, stochastic turbulence, and the passage from particle systems to continuum descriptions of fluctuations, transport, and universality.

The organizers are Benjamin Gess (TU Berlin and the Max Planck Institute for Mathematics in the Sciences, Leipzig) and Adrian Martini (TU Berlin). The meeting will be held at IMoS, Fasanenstraße 89, 10623 Berlin.

Poster submissions: please send a title and abstract to adrian.martini@tu-berlin.de by 15 January 2027. Decisions will be communicated in February 2027.

The speaker list and further information are available on the conference website.

Publications

Exponential convergence rates for momentum stochastic gradient descent in the overparametrized setting
Byadmin 7 February 20239 October 2026

Published · Mathematical programming, (2026). We prove explicit bounds on the exponential rate of convergence for the momentum stochastic gradient descent scheme (MSGD) for arbitrary, fixed hyperparameters (learning rate, friction parameter) and its continuous-in-time counterpart in the…

Read More Exponential convergence rates for momentum stochastic gradient descent in the overparametrized setting
Member Publication Archive

Density bounds for solutions to differential equations driven by Gaussian rough paths
Byadmin 7 December 201728 September 2026

Published · Journal of theoretical probability, 33 (2020) 2, pp. 611-648. We consider finite dimensional rough differential equations driven by centered Gaussian processes. Combining Malliavin calculus, rough paths techniques and interpolation inequalities, we establish upper bounds on the density of the corresponding solution…

Read More Density bounds for solutions to differential equations driven by Gaussian rough paths
Publications

Finite speed of propagation and waiting time phenomena for stochastic porous media equations with nonlinear conservative noise
Byadmin 31 August 202627 September 2026

Starting from localized energy estimates, we prove finite speed of propagation for kinetic solutions to stochastic porous media equations with nonlinear conservative noise, the existence and uniqueness of which has recently been established. In particular, we propose a novel iteration technique which…

Read More Finite speed of propagation and waiting time phenomena for stochastic porous media equations with nonlinear conservative noise
Publications

Conservative stochastic PDEs on the whole space
Byadmin 30 September 20249 October 2026

Published · Stochastics and partial differential equations : analysis and computations, 14 (2026) 1, pp. 350-388. The purpose of this paper is to establish a well-posedness theory for conservative stochastic partial differential equations on the whole space. This class of stochastic PDEs arises in fluctuating hydrodynamics, and includes…

Read More Conservative stochastic PDEs on the whole space
Publications

Fluctuation behaviour for interacting particle systems with common noise
Byadmin 7 April 20259 October 2026

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…

Read More Fluctuation behaviour for interacting particle systems with common noise
Publications

The stochastic Cahn-Hilliard equation in critical spaces
Byadmin 21 August 202627 September 2026

We study stochastic Cahn-Hilliard equations in bounded smooth domains with a double-well potential, transport-type noise, and natural Neumann boundary conditions in dimensions $d\le 4$. By employing stochastic maximal regularity techniques and deriving suitable energy estimates, we prove local and global well-posedness. The…

Read More The stochastic Cahn-Hilliard equation in critical spaces

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