Correlation Dimension as the Large Deviation for Distribution of Distances between Two Points on an Embedded Manifold

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概要

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• The correlation integraxl is eqttivalent to the distr'ibution of distances between two points onany dimensional tnanifold reconstructed by the eu?abedding method frorn arny tinae series data.The correlation integral agrees witlu the law of' large nuraabers arrd has converged distributiotain the large-nunaber limit of the embedding dirnension. This converged distribtrtion does notobey the classical central limit tlaeorena. The converging process of the correlation integral isnot visible. Therefore, we utilize the distribtttion density of the distances between two points.The properties of distribtrtion density for distances between two points are considered and it isconcluded that the correlation diunension proposed Icy Grassberger and Procaccia is an exponentof power on the large deviation of distribtttion density of distances between two points.

• 社団法人日本物理学会の論文
• 1998-10-15

著者

• YAMAGUCHI Hideki

  Department of Applied Physics, School of Engineering, The University of Tokyo

• Nagai Yoshinori

  Center For Information Science And School Of Political And Economic Sciences Kokushikan University

• Yamaguchi Hideki

  Department Of Applied Physics School Of Engineering The University Of Tokyo

• Yamaguchi Hideki

  Department Of Commerce And Economics Junior College Nihon University

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