Homotopy probability theory I

@article{DrummondCole2013HomotopyPT,
  title={Homotopy probability theory I},
  author={Gabriel C. Drummond-Cole and Jae-Suk Park and John Terilla},
  journal={Journal of Homotopy and Related Structures},
  year={2013},
  volume={10},
  pages={425-435}
}
This is the first of two papers that introduce a deformation theoretic framework to explain and broaden a link between homotopy algebra and probability theory. In this paper, cumulants are proved to coincide with morphisms of homotopy algebras. The sequel paper outlines how the framework presented here can assist in the development of homotopy probability theory, allowing the principles of derived mathematics to participate in classical and noncommutative probability theory. 
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This is the second of two papers that introduce a deformation theoretic framework to explain and broaden a link between homotopy algebra and probability theory. This paper outlines how the framework…
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