Preprint: Graph-to-local limit for the nonlocal interaction equation

6 June 2023

Together with Antonio Esposito and Georg Heinze, we study a class of nonlocal partial differential equations presenting a tensor-mobility, in space, obtained asymptotically from nonlocal dynamics on localising infinite graphs. Our strategy relies on the variational structure of both equations, being a Riemannian and Finslerian gradient flow, respectively. More precisely, we prove that weak solutions of the nonlocal interaction equation on graphs converge to weak solutions of the aforementioned class of nonlocal interaction equation with a tensor-mobility in the Euclidean space.

A geometric graph obtained as iid. samples from a distribution supported on a two-dimensional submanifold embedded in three dimensions with edge-weights given by the distance to the neighbors.

Now published in J. Math. Pures Appl. 194, 103663 (2025).

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