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math.PR2018★ 37 cited
A Law of Large Numbers and Large Deviations for interacting diffusions on Erdős-Rényi graphs
Fabio Coppini, Helge Dietert, Giambattista Giacomin
We consider a class of particle systems described by differential equations (both stochastic and deterministic), in which the interaction network is determined by the realization o…
math.PR2015★ 3 cited
Convergence to equilibrium for the kinetic Fokker-Planck equation on the torus
Helge Dietert, Josephine Evans, Thomas Holding
We study convergence to equilibrium for the kinetic Fokker-Planck equation on the torus. Solving the stochastic differential equation, we show exponential convergence in the Monge-…
math.PR2014★ 5 cited
Characterisation of gradient flows on finite state Markov chains
Helge Dietert
In his 2011 work, Maas has shown that the law of any time-reversible continuous-time Markov chain with finite state space evolves like a gradient flow of the relative entropy with…