Nathanaël Berestycki works in probability theory, connecting stochastic motion with random geometry. His University of Vienna homepage identifies research on Brownian motion, the Gaussian free field, Liouville quantum gravity and interacting particle systems.[ref]
https://homepage.univie.ac.at/nathanael.berestycki/. Author homepage, What I do and institutional identification
With Christophe Garban and Arnab Sen, he introduced a topology for the coalescing Brownian flow and obtained convergence from coalescing random walks under finite variance of the increments. The state-space choice makes the continuum limit accessible without stronger moment assumptions previously needed in other descriptions.[ref]
Coalescing Brownian flows: A new approach by Nathanaël Berestycki and others. Abstract and Introduction: comparison of moment assumptions and flow topology
A useful distinction is between convergence of finitely many trajectories and convergence of a whole random flow. Starting particles at many locations creates a shared pattern of meetings and mergers. A continuum description has to preserve the consistency of those histories, rather than merely fit the distribution of one endpoint.
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