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pro vyhledávání: '"Ledger, Sean"'
Autor:
Ledger, Sean, Sojmark, Andreas
We derive two weak formulations for the supercooled Stefan problem with transport noise on a half-line: one captures a continuously evolving system, while the other resolves blow-ups by allowing for jump discontinuities in the evolution of the temper
Externí odkaz:
http://arxiv.org/abs/2409.20421
Akademický článek
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Autor:
Ledger, Sean, Sojmark, Andreas
We present a simple uniqueness argument for a collection of McKean-Vlasov problems that have seen recent interest. Our first result shows that, in the weak feedback regime, there is global uniqueness for a very general class of random drivers. By wea
Externí odkaz:
http://arxiv.org/abs/1811.12356
We introduce two discrete models of a collection of colliding particles with stored momentum and study the asymptotic growth of the mean-square displacement of an active particle. We prove that the models are superdiffusive in one dimension (with pow
Externí odkaz:
http://arxiv.org/abs/1809.03257
Autor:
Ledger, Sean, Sojmark, Andreas
We extend a model of positive feedback and contagion in large mean-field systems, by introducing a common source of noise driven by Brownian motion. Although the driving dynamics are continuous, the positive feedback effect can lead to `blow-up' phen
Externí odkaz:
http://arxiv.org/abs/1807.05126
In the randomly-oriented Manhattan lattice, every line in $\mathbb{Z}^d$ is assigned a uniform random direction. We consider the directed graph whose vertex set is $\mathbb{Z}^d$ and whose edges connect nearest neighbours, but only in the direction f
Externí odkaz:
http://arxiv.org/abs/1802.01558
We study a McKean--Vlasov equation arising from a mean-field model of a particle system with positive feedback. As particles hit a barrier they cause the other particles to jump in the direction of the barrier and this feedback mechanism leads to the
Externí odkaz:
http://arxiv.org/abs/1801.07703
Autor:
Ledger, Sean
The purpose of this thesis is to develop techniques for analysing interacting particle systems on the half-line. When the number of particles becomes large, stochastic partial differential equations (SPDEs) with Dirichlet boundary conditions will be
Externí odkaz:
http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.684934
Autor:
Hambly, Ben, Ledger, Sean
Publikováno v:
Ann. Appl. Probab. Volume 27, Number 5 (2017), 2698-2752
We study a finite system of diffusions on the half-line, absorbed when they hit zero, with a correlation effect that is controlled by the proportion of the processes that have been absorbed. As the number of processes in the system becomes large, the
Externí odkaz:
http://arxiv.org/abs/1605.00669
Autor:
Ledger, Sean
Publikováno v:
Electronic Communications in Probability, Vol. 21, No. 34, pp 1-11, 2016
Skorokhod's M1 topology is defined for c\`adl\`ag paths taking values in the space of tempered distributions (more generally, in the dual of a countably Hilbertian nuclear space). Compactness and tightness characterisations are derived which allow us
Externí odkaz:
http://arxiv.org/abs/1509.02855