The McMillan Theorem for Colored Branching Processes and Dimensions of Random Fractals

The McMillan Theorem for Colored Branching Processes and Dimensions of Random Fractals

For the simplest colored branching process, we prove an analog to the McMillan theorem and calculate the Hausdorff dimensions of random fractals defined in terms of the limit behavior of empirical measures generated by finite genetic lines. In this setting, the role of Shannon’s entropy is played by...

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Bibliographic Details
Main Author: Victor Bakhtin
Format: Article
Language:English
Published: MDPI AG 2014-12-01
Series:Entropy
Subjects:
colored branching process
random fractal
Hausdorff dimension
spectral potential
Kullback action
Billingsley–Kullback entropy
basin of a probability measure
maximal dimension principle
Online Access:http://www.mdpi.com/1099-4300/16/12/6624

Internet

http://www.mdpi.com/1099-4300/16/12/6624

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