Benjamin Gess and Johannes Müller have released “The Advective Fisher–Rao Geometry of Deterministic Measure Transport.” The work introduces an advective Fisher–Rao metric for optimization tasks on paths of probability measures governed by the continuity equation and relates it to large deviations and optimal transport.
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…
Published · Communications on pure and applied mathematics, 70 (2017) 8, pp. 1562-1597. We study the long-time behavior and the regularity of pathwise entropy solutions to stochastic scalar conservation laws with random in time spatially homogeneous fluxes and periodic initial data. We prove that the…
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 · Transactions of the American Mathematical Society, (2026). We study asymptotic expansions of the Euclidean $Φ^4_2$-measure in the low-temperature regime. In particular, this extends the asymptotic expansions of Gaussian function space integrals developed in Schilder (1966) and Ellis and Rosen…
The stated application deadline for this FluCo postdoctoral position was 11 September 2026.
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…
