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Updated: Jan 19, 2026

Stable Aqueous Suspensions of Manganese Ferrite Clusters with Tunable Nanoscale Dimension and Composition
Published on: February 5, 2022
Emergence of patterns in random processes. III. Clustering in higher dimensions
1School of Natural Sciences, Institute for Advanced Study, Princeton, New Jersey 08540, USA and Department of Earth & Space Sciences, Department of Physics & Astronomy, and Department of Mathematics, University of California, Los Angeles, California 90095, USA.
Abstract:
Newman et al. [Phys. Rev. E 86, 026103 (2012)10.1103/PhysRevE.86.026103] showed that points uniformly distributed as independent and identically distributed random variables with nearest-neighbor interactions form clusters with a mean number of three points in each. Here, we extend our analysis to higher dimensions, ultimately going to infinite dimensions, and we show that the mean number of points per cluster rises monotonically with a limiting value of four.
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