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Displacement convexity for the entropy in semi-discrete non-linear Fokker–Planck equations

Published online by Cambridge University Press:  10 January 2018

Department of Mathematics, Imperial College London, London SW7 2AZ, UK email:
Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstraße 8-10, 1040 Wien, Austria email:
Departamento de Matemática – IMECC, Universidade Estadual de Campinas, Campinas-SP, Brazil email:
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The displacement λ-convexity of a non-standard entropy with respect to a non-local transportation metric in finite state spaces is shown using a gradient flow approach. The constant λ is computed explicitly in terms of a priori estimates of the solution to a finite-difference approximation of a non-linear Fokker–Planck equation. The key idea is to employ a new mean function, which defines the Onsager operator in the gradient flow formulation.

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© Cambridge University Press 2018


The first author was partially supported by the Royal Society via a Wolfson Research Merit Award and the EPSRC Grant EP/P031587/1. The second author acknowledges partial support from the Austrian Science Fund (FWF), Grants P22108, P24304, F65 and W1245. The last author acknowledges the support from the São Paulo Research Foundation (FAPESP), Grant 2015/20962-7.


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