TY - JOUR
T1 - Spatial Statistics of Apollonian Gaskets
AU - Chen, Weiru
AU - Jiao, Mo
AU - Kessler, Calvin
AU - Malik, Amita
AU - Zhang, Xin
N1 - Funding Information:
This work is supported by the National Grant DMS-1449269.
Funding Information:
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. Figures?10 and 11 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. This work is supported by the National Science Foundation Grant DMS-1449269.
Publisher Copyright:
© 2017, © 2017 Taylor & Francis Group, LLC.
PY - 2019/7/3
Y1 - 2019/7/3
N2 - 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.
AB - 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.
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U2 - 10.1080/10586458.2017.1385037
DO - 10.1080/10586458.2017.1385037
M3 - Article
AN - SCOPUS:85035791463
SN - 1058-6458
VL - 28
SP - 263
EP - 270
JO - Experimental Mathematics
JF - Experimental Mathematics
IS - 3
ER -