[图书][B] Optimal transport: old and new
C Villani - 2009 - Springer
At the close of the 1980s, the independent contributions of Yann Brenier, Mike Cullen and
John Mather launched a revolution in the venerable field of optimal transport founded by G …
John Mather launched a revolution in the venerable field of optimal transport founded by G …
Entropic measure and Wasserstein diffusion
MK von Renesse, KT Sturm - 2009 - projecteuclid.org
We construct a new random probability measure on the circle and on the unit interval which
in both cases has a Gibbs structure with the relative entropy functional as Hamiltonian. It …
in both cases has a Gibbs structure with the relative entropy functional as Hamiltonian. It …
Well-posedness of the Dean–Kawasaki and the nonlinear Dawson–Watanabe equation with correlated noise
B Fehrman, B Gess - Archive for Rational Mechanics and Analysis, 2024 - Springer
In this paper we prove the well-posedness of the generalized Dean–Kawasaki equation
driven by noise that is white in time and colored in space. The results treat diffusion …
driven by noise that is white in time and colored in space. The results treat diffusion …
Dean-Kawasaki dynamics: ill-posedness vs. triviality
V Konarovskyi, T Lehmann, MK von Renesse - 2019 - projecteuclid.org
Electron. Commun. Probab. 24 (2019), no. 8, https://doi.org/10.1214/19-ECP208 Page 1
Electron. Commun. Probab. 24 (2019), no. 8, 1–9. https://doi.org/10.1214/19-ECP208 ISSN …
Electron. Commun. Probab. 24 (2019), no. 8, 1–9. https://doi.org/10.1214/19-ECP208 ISSN …
Conservative SPDEs as fluctuating mean field limits of stochastic gradient descent
The convergence of stochastic interacting particle systems in the mean-field limit to solutions
of conservative stochastic partial differential equations is established, with optimal rate of …
of conservative stochastic partial differential equations is established, with optimal rate of …
On Dean–Kawasaki dynamics with smooth drift potential
V Konarovskyi, T Lehmann, M von Renesse - Journal of Statistical Physics, 2020 - Springer
On Dean–Kawasaki Dynamics with Smooth Drift Potential | SpringerLink Skip to main content
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Density fluctuations in weakly interacting particle systems via the dean-kawasaki equation
F Cornalba, J Fischer, J Ingmanns, C Raithel - arXiv preprint arXiv …, 2023 - arxiv.org
The Dean-Kawasaki equation-one of the most fundamental SPDEs of fluctuating
hydrodynamics-has been proposed as a model for density fluctuations in weakly interacting …
hydrodynamics-has been proposed as a model for density fluctuations in weakly interacting …
A Regularized Dean--Kawasaki Model: Derivation and Analysis
The Dean--Kawasaki model consists of a nonlinear stochastic partial differential equation
featuring a conservative, multiplicative, stochastic term with non-Lipschitz coefficient, driven …
featuring a conservative, multiplicative, stochastic term with non-Lipschitz coefficient, driven …
Modified massive Arratia flow and Wasserstein diffusion
V Konarovskyi, MK von Renesse - Communications on pure …, 2019 - Wiley Online Library
Extending previous work by the first author we present a variant of the Arratia flow, which
consists of a collection of coalescing Brownian motions starting from every point of the unit …
consists of a collection of coalescing Brownian motions starting from every point of the unit …
Well-Posedness for Dean-Kawasaki Models of Vlasov-Fokker-Planck Type
F Müller, M von Renesse, J Zimmer - arXiv preprint arXiv:2411.14334, 2024 - arxiv.org
We consider systems of interacting particles which are described by a second order
Langevin equation, ie, particles experiencing inertia. We introduce an associated equation …
Langevin equation, ie, particles experiencing inertia. We introduce an associated equation …