https://orcid.org/0000-0001-7247-2785
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ABSTRACT
Apollonian gaskets are formed by repeatedly filling the interstices between four mutually tangent circles with further tangent circles. We experimentally study the nearest neighbor spacing, pair correlation, and electrostatic energy of centers of circles from Apollonian gaskets. Even though the centers of these circles are not uniformly distributed in any “ambient” space, after proper normalization, all these statistics seem to exhibit certain interesting limiting behaviors.
AMS Subject Classification:
Acknowledgments
Our work is a product of a research project of the Illinois Geometry Lab (IGL) for the Spring, 2017 semester. The first-three authors are the undergraduate members of our IGL team, the fourth one is the graduate mentor, and the last author is the faculty mentor for the project. and are due to Lori Gardi. We are also thankful to Professors Florin Boca, Alex Kontorovich, and Zeev Rudnick for detailed comments and corrections on a previous draft.
Funding
This work is supported by the National Science Foundation Grant DMS-1449269.