Dimensions of the popcorn graph
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The 'popcorn function' is a well-known and important example in real analysis with many interesting features. We prove that the box dimension of the graph of the popcorn function is 4/3, as well as computing the Assouad dimension and Assouad spectrum. The main ingredients include Duffin-Schaeffer type estimates from Diophantine approximation and the Chung-Erdős inequality from probability theory.
Chen , H , Fraser , J & Yu , H 2022 , ' Dimensions of the popcorn graph ' , Proceedings of the American Mathematical Society , vol. 150 , pp. 4729-4742 . https://doi.org/10.1090/proc/15729
Proceedings of the American Mathematical Society
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DescriptionFunding: H. Chen is thankful for the excellent atmosphere for research provided by the University of St Andrews. H. Chen was funded by China Scholarship Council (File No. 201906150102) and NSFC (No. 11601161, 11771153 and 11871227). J. M. Fraser was supported by an EPSRC Standard Grant (EP/R015104/1) and a Leverhulme Trust Research Project Grant (RPG-2019-034). H. Yu was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 803711), and indirectly by Corpus Christi College, Cambridge.
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