Publications and highlights associated with Benjamin Gess.
Published · The annals of applied probability, 35 (2025) 1, pp. 481-522. We study scaling limits of the weakly driven Zhang and the Bak-Tang-Wiesenfeld (BTW) model for self-organized criticality. We show that the weakly driven Zhang model converges to a stochastic partial differential equation…
Published · Journal of evolution equations, 25 (2025) 2, p. 42. Stabilization and sufficient conditions for mixing by stochastic transport are shown. More precisely, given a second order linear operator with possibly unstable eigenvalues on a smooth compact Riemannian manifold, it is shown…
Published · IMA journal of numerical analysis, 44 (2024) 4, pp. 2090-2137. We study a general class of singular degenerate parabolic stochastic partial differential equations (SPDEs) which include, in particular, the stochastic porous medium equations and the stochastic fast diffusion equation. We propose a…
Published · Stochastics and dynamics, 22 (2022) 7, p. 2240023. A new mechanism leading to a random version of Burgers’ equation is introduced: it is shown that the Totally Asymmetric Exclusion Process in discrete time (TASEP) can be understood as an intrinsically…
Published · Archive for rational mechanics and analysis, 242 (2021) 1, pp. 179-234. We prove the existence of nonnegative martingale solutions to a class of stochastic degenerate-parabolic fourth-order PDEs arising in surface-tension driven thin-film flow influenced by thermal noise. The construction applies to a range…
Published · Communications in mathematical physics, 407 (2026) 4, p. 74. In this paper, we provide a continuum model for the fluctuations of the symmetric simple exclusion process about its hydrodynamic limit. The model is based on an approximating sequence of stochastic PDEs…
Published · Annales de l’Institut Henri Poincaré / B : Probabilites et statistiques, 57 (2021) 4, pp. 2354-2371. The existence of martingale solutions for stochastic porous media equations driven by nonlinear multiplicative space-time white noise is established in spatial dimension one. The Stroock-Varopoulos inequality is identified as a key tool…
Published · Inventiones mathematicae, 234 (2023) 2, pp. 573-636. Large deviations of conservative interacting particle systems, such as the zero range process, about their hydrodynamic limit and their respective rate functions lead to the analysis of the skeleton equation; a degenerate…
Published · Stochastics and Dynamics 20(6), 2040006 (2020). We prove uniform synchronisation by noise with rates for the stochastic quantisation equation in dimensions two and three. The proof relies on a combination of coming down from infinity estimates and the…
Published · Journal of differential equations, 269 (2020) 4, pp. 3414-3455. We prove the existence of random dynamical systems and random attractors for a large class of locally monotone stochastic partial differential equations perturbed by additive Lévy noise. The main result is applicable…
Published · SIAM journal on mathematical analysis, 52 (2020) 5, pp. 4524-4564. The long time behaviour of solutions to stochastic porous media equations on smooth bounded domains with Dirichlet boundary data is studied. Based on weighted $L^{1}$-estimates the existence and uniqueness of invariant measures…
Published · Stochastic processes and their applications, 130 (2020) 12, pp. 7260-7302. We consider the stochastic thin-film equation with colored Gaussian Stratonovich noise in one space dimension and establish the existence of nonnegative weak (martingale) solutions. The construction is based on a Trotter-Kato-type decomposition…
