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Article: Statistical regularity of Apollonian gaskets
Title | Statistical regularity of Apollonian gaskets |
---|---|
Authors | |
Issue Date | 2021 |
Publisher | Oxford University Press. The Journal's web site is located at http://imrn.oxfordjournals.org |
Citation | International Mathematics Research Notices, 2021, v. 2021 n. 2, p. 1055-1095 How to Cite? |
Abstract | Apollonian gaskets are formed by repeatedly filling the gaps between three mutually tangent circles with further tangent circles. In this paper we give explicit formulas for the limiting pair correlation and the limiting nearest neighbor spacing of centers of circles from a fixed Apollonian gasket. These are corollaries of the convergence of moments that we prove. The input from ergodic theory is an extension of Mohammadi–Oh’s theorem on the equidisribution of expanding horospheres in the frame fundles of infinite volume hyperbolic spaces. |
Persistent Identifier | http://hdl.handle.net/10722/289727 |
ISSN | 2023 Impact Factor: 0.9 2023 SCImago Journal Rankings: 1.337 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Zhang, X | - |
dc.date.accessioned | 2020-10-22T08:16:36Z | - |
dc.date.available | 2020-10-22T08:16:36Z | - |
dc.date.issued | 2021 | - |
dc.identifier.citation | International Mathematics Research Notices, 2021, v. 2021 n. 2, p. 1055-1095 | - |
dc.identifier.issn | 1073-7928 | - |
dc.identifier.uri | http://hdl.handle.net/10722/289727 | - |
dc.description.abstract | Apollonian gaskets are formed by repeatedly filling the gaps between three mutually tangent circles with further tangent circles. In this paper we give explicit formulas for the limiting pair correlation and the limiting nearest neighbor spacing of centers of circles from a fixed Apollonian gasket. These are corollaries of the convergence of moments that we prove. The input from ergodic theory is an extension of Mohammadi–Oh’s theorem on the equidisribution of expanding horospheres in the frame fundles of infinite volume hyperbolic spaces. | - |
dc.language | eng | - |
dc.publisher | Oxford University Press. The Journal's web site is located at http://imrn.oxfordjournals.org | - |
dc.relation.ispartof | International Mathematics Research Notices | - |
dc.rights | Post-print: This is a pre-copy-editing, author-produced PDF of an article accepted for publication in [insert journal title] following peer review. The definitive publisher-authenticated version [insert complete citation information here] is available online at: xxxxxxx [insert URL that the author will receive upon publication here]. | - |
dc.title | Statistical regularity of Apollonian gaskets | - |
dc.type | Article | - |
dc.identifier.email | Zhang, X: xz27@hku.hk | - |
dc.identifier.authority | Zhang, X=rp02608 | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1093/imrn/rnz241 | - |
dc.identifier.scopus | eid_2-s2.0-85107759269 | - |
dc.identifier.hkuros | 317199 | - |
dc.identifier.volume | 2021 | - |
dc.identifier.issue | 2 | - |
dc.identifier.spage | 1055 | - |
dc.identifier.epage | 1095 | - |
dc.identifier.isi | WOS:000629746800007 | - |
dc.publisher.place | United Kingdom | - |
dc.identifier.issnl | 1073-7928 | - |