Mean-field limits for some Riesz interaction gradient flows

The present work extends the result [51] valid for the 2-dimensional Coulomb gases to the case of general dimension d and of Riesz gases with power-law interactions with power s ∈

Also convergence to equilibrium (through a contraction argument in W 2 distance) and time uniform deviation bounds were obtained in [4] for solutions to the (now space

Keywords: stochastic particle systems, mean-field limit, propagation of chaos, stochas- tic partial differential equations, Cucker-Smale model, collective

SOBOLEV, The quasi-classical asymptotics of local Riesz means for the Schrödinger operator in a strong homogeneous magnetic field, Duke Math. SOBOLEV, The sum

It has been noted in [10] that the difficulty arises in the application of the classical L p - theory of Caldéron-Zygmund, since Riesz transforms are singular integral operators..

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Riesz [7] showed some properties of the integral of fractional order which is a generalization of the Riemann integral to more than

Taylor, Potential theory on Lipschitz domains in Riemannian manifolds: Sobolev-Besov space results and the Poisson problem, J. Pazy, Semigroups of Linear Operators and Applications