Gravitational Allocation and Internal DLA

Yuval Peres
University of California, Berkeley (UC Berkeley)

Given a Poisson process of stars, Chandrasekhar (1942) discovered that Newtonian gravitational force is convergent a.s. in dimension at least 3, and has a stable law. We use this force (in the infinite friction limit) to partition space into basins of attraction which have equal volumes. We prove that the diameters of the basins have exponential tail. (Joint work with S. Chatterjee, R. Peled, D. Romik). In a separate work with L. Levine, we prove that internal diffusion limited aggregation with multiple sources has a scaling limit. Both works are linked to a free boundary problem for the Laplacian.

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