20 citations · 40 across the 7 of their papers we have counts for
7 papers
Quantitative Universal Approximation Bounds for Deep Belief Networks
Julian Sieber, Johann Gehringer
We show that deep belief networks with binary hidden units can approximate any multivariate probability density under very mild integrability requirements on the parental density o…
On the (Non-)Stationary Density of Fractional-Driven Stochastic Differential Equations
Xue-Mei Li, Fabien Panloup, Julian Sieber
We investigate the stationary measure of SDEs driven by additive fractional noise with any Hurst parameter and establish that admits a smooth Lebesgue density obeying both…
Mild Stochastic Sewing Lemma, SPDE in Random Environment, and Fractional Averaging
Xue-Mei Li, Julian Sieber
Our first result is a stochastic sewing lemma with quantitative estimates for mild incremental processes, with which we study SPDEs driven by fractional Brownian motions in a rando…
Functional Limit Theorems for Volterra Processes and Applications to Homogenization
Johann Gehringer, Xue-Mei Li, Julian Sieber
We prove an enhanced limit theorem for additive functionals of a multi-dimensional Volterra process in the rough path topology. As an application, we establish we…
Slow-Fast Systems with Fractional Environment and Dynamics
Xue-Mei Li, Julian Sieber
We prove a fractional averaging principle for interacting slow-fast systems. The mode of convergence is in Hölder norm in probability. The main technical result is a quenched ergod…
Formulae for the Derivative of the Poincaré Constant of Gibbs Measures
Julian Sieber
We establish formulae for the derivative of the Poincaré constant of Gibbs measures on both compact domains and all of . As an application, we show that if the (not necessari…
Bounds on the bipartite entanglement entropy for oscillator systems with or without disorder
Vincent Beaud, Julian Sieber, Simone Warzel
We give a direct alternative proof of an area law for the entanglement entropy of the ground state of disordered oscillator systems---a result due to Nachtergaele, Sims and Stolz.…