Propagation of chaos for the Vlasov-Poisson-Fokker-Planck equation with a polynomial cut-off
We consider a N-particle system interacting through the Newtonian potential with a polynomial cut-off in the presence of noise in velocity. We rigorously prove the propagation of chaos for this interacting stochastic particle system. Taking the cut-off like N−δ with δ<1/d in the force, we provide...
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| Format: | Journal article |
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World Scientific Publishing
2018
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| _version_ | 1797060818582372352 |
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| author | Carrillo de la Plata, JA Choi, YP Salem, S |
| author_facet | Carrillo de la Plata, JA Choi, YP Salem, S |
| author_sort | Carrillo de la Plata, JA |
| collection | OXFORD |
| description | We consider a N-particle system interacting through the Newtonian potential with a polynomial cut-off in the presence of noise in velocity. We rigorously prove the propagation of chaos for this interacting stochastic particle system. Taking the cut-off like N−δ with δ<1/d in the force, we provide a quantitative error estimate between the empirical measure associated to that N-particle system and the solutions of the d-dimensional Vlasov–Poisson–Fokker–Planck (VPFP) system. We also study the propagation of chaos for the Vlasov–Fokker–Planck equation with less singular interaction forces than the Newtonian one. |
| first_indexed | 2024-03-06T20:22:17Z |
| format | Journal article |
| id | oxford-uuid:2e39f6fd-a943-4616-a02e-03438b713f7b |
| institution | University of Oxford |
| last_indexed | 2024-03-06T20:22:17Z |
| publishDate | 2018 |
| publisher | World Scientific Publishing |
| record_format | dspace |
| spelling | oxford-uuid:2e39f6fd-a943-4616-a02e-03438b713f7b2022-03-26T12:47:42ZPropagation of chaos for the Vlasov-Poisson-Fokker-Planck equation with a polynomial cut-offJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:2e39f6fd-a943-4616-a02e-03438b713f7bSymplectic ElementsWorld Scientific Publishing2018Carrillo de la Plata, JAChoi, YPSalem, SWe consider a N-particle system interacting through the Newtonian potential with a polynomial cut-off in the presence of noise in velocity. We rigorously prove the propagation of chaos for this interacting stochastic particle system. Taking the cut-off like N−δ with δ<1/d in the force, we provide a quantitative error estimate between the empirical measure associated to that N-particle system and the solutions of the d-dimensional Vlasov–Poisson–Fokker–Planck (VPFP) system. We also study the propagation of chaos for the Vlasov–Fokker–Planck equation with less singular interaction forces than the Newtonian one. |
| spellingShingle | Carrillo de la Plata, JA Choi, YP Salem, S Propagation of chaos for the Vlasov-Poisson-Fokker-Planck equation with a polynomial cut-off |
| title | Propagation of chaos for the Vlasov-Poisson-Fokker-Planck equation with a polynomial cut-off |
| title_full | Propagation of chaos for the Vlasov-Poisson-Fokker-Planck equation with a polynomial cut-off |
| title_fullStr | Propagation of chaos for the Vlasov-Poisson-Fokker-Planck equation with a polynomial cut-off |
| title_full_unstemmed | Propagation of chaos for the Vlasov-Poisson-Fokker-Planck equation with a polynomial cut-off |
| title_short | Propagation of chaos for the Vlasov-Poisson-Fokker-Planck equation with a polynomial cut-off |
| title_sort | propagation of chaos for the vlasov poisson fokker planck equation with a polynomial cut off |
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