7 citations · 9 across the 11 of their papers we have counts for
11 papers
Effective Lagrangian regularity and the uniqueness threshold for random Hölder velocity fields
Maria Colombo, Elias Hess-Childs, Keefer Rowan
We study the behavior of the ordinary differential equations, flow maps, and continuity equations associated to autonomous random velocity fields that admit a natural multiscale fi…
Sharp pathwise nonuniqueness for additive SDEs
Elias Hess-Childs, Keefer Rowan
We construct a family of velocity fields demonstrating the sharpness of the classical Zvonkin--Veretennikov--Davie strong well-posedness by noise regime. We consider stochastic dif…
Radon--Wasserstein Gradient Flows for Interacting-Particle Sampling in High Dimensions
Elias Hess-Childs, Dejan Slepčev, Lantian Xu
Gradient flows of the Kullback--Leibler (KL) divergence, such as the Fokker--Planck equation and Stein Variational Gradient Descent, evolve a distribution toward a target density k…
Another look at regularity in transport-commutator estimates
Elias Hess-Childs, Matthew Rosenzweig, Sylvia Serfaty
We are interested in how regular a transport velocity field must be in order to control Riesz-type commutators. Estimates for these commutators play a central role in the analysis…
A sharp commutator estimate for all Riesz modulated energies
Elias Hess-Childs, Matthew Rosenzweig, Sylvia Serfaty
We prove a functional inequality in any dimension controlling the derivative along a transport of the Riesz modulated energy in terms of the modulated energy itself. This modulated…
Turbulent and intermittent phenomena in a universal total anomalous dissipator
Elias Hess-Childs, Keefer Rowan
For all , we construct an explicit divergence-free vector field that exhibits universal anomalous (total) dissipation, acceler…
Divergence-free drifts decrease concentration
Elias Hess-Childs, Renaud Raquépas, Keefer Rowan
We show that bounded divergence-free vector fields decrease the ''concentration'', quantified by the modulus of absolute contin…
A universal total anomalous dissipator
Elias Hess-Childs, Keefer Rowan
For all , we construct an explicit divergence-free vector field so that the solutions to the drift-diffusion equ…
Large deviation principles for singular Riesz-type diffusive flows
Elias Hess-Childs
We combine hydrodynamic and modulated energy techniques to study the large deviations of systems of particles with pairwise singular repulsive interactions and additive noise. Spec…
Higher-order propagation of chaos in for interacting diffusions
Elias Hess-Childs, Keefer Rowan
In this paper, we study diffusions with bounded pairwise interaction. We show for the first time propagation of chaos on arbitrary time horizons in a stronger -based distance,…
On the Strong Attraction Limit for a Class of Nonlocal Interaction Energies
Almut Burchard, Rustum Choksi, Elias Hess-Childs
This note concerns the problem of minimizing a certain family of non-local energy functionals over measures on , subject to a mass constraint, in a strong attraction…