The approach à la Jordan-Kinderlehrer-Otto to a vast class of evolutionary problems, interpreted as gradient flows in Wasserstein spaces, was extended by Maas and Mielke to Markov chains via the introduction of Benamou-Brenier type distances. Nonetheless, the study of the microscopic origin of jump processes by means of large deviations theory suggests that such processes possess a generalized gradient-flow structure based on non-homogeneous dissipation potentials that do not give rise to any metric structure.
This talk revolves around the generalized gradient-flow structure that we have proposed for these processes in collaboration with Mark Peletier, Giuseppe Savaré and Oliver Tse. To build it, we have introduced a suitable ‘dynamical-variational’ transport cost that induces a notion of length. Based on it, we can set forth an extended version of the Minimizing Movement scheme. We show the convergence of the discrete solutions arising from the time-incremental minimization scheme, to a curve fulfilling a suitable ‘non-metric’ gradient flow formulation for the original jump process.
Link zoom: https://univr.zoom.us/j/87599248955
Meeting ID: 875 9924 8955
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