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https://hdl.handle.net/2142/72528
Description
Title
Climbing Mount Probable
Author(s)
Harper, Marc Allen
Issue Date
2009
Doctoral Committee Chair(s)
Leininger, Christopher J.
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Theoretical Mathematics
Abstract
This work attempts to explain the relationships between natural selection, information theory, and statistical inference. In particular, a geometric formulation of information theory known as information geometry and its deep connections to evolutionary game theory inform the role of natural selection in evolutionary processes. The goals of this work may be stated as (1) to show that a significant collection of important results in evolutionary dynamics can be interpreted elegantly in the context of information theory, and (2) to generalize the framework to study dynamics other than the replicator equation.
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