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Minimum memory for generating rare events.

Cina Aghamohammadi1, James P Crutchfield1

  • 1Complexity Sciences Center and Department of Physics, University of California at Davis, One Shields Avenue, Davis, California 95616, USA.

Physical Review. E
|April 19, 2017
PubMed
Summary

This study classifies rare events in stochastic processes, revealing the minimum memory needed for event generation. It also finds a classical-quantum ambiguity in process fluctuations, impacting generator analysis.

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Area of Science:

  • Complex Systems
  • Information Theory
  • Statistical Mechanics

Background:

  • Stochastic processes are fundamental to modeling random phenomena.
  • Understanding rare events is crucial in fields like finance and physics.
  • Memory in processes affects their predictability and generation.

Purpose of the Study:

  • To classify and analyze rare events in structured, memoryful stochastic processes.
  • To develop methods for generating rare events from a given process.
  • To investigate the relationship between process fluctuations and classical-quantum ambiguity.

Main Methods:

  • Classification of rare events in stochastic processes.
  • Construction of a new process from the rare events of a given process.
  • Derivation of an expression for minimum memory requirements.
  • Analysis of process fluctuations for classical-quantum ambiguity.

Main Results:

  • A method to construct a process generating rare events of another process.
  • An expression for the minimum memory required to generate rare events.
  • Demonstration that classical-quantum ambiguity of simplicity extends to process fluctuations.

Conclusions:

  • The study provides a framework for understanding and generating rare events in complex systems.
  • Minimum memory requirements for rare event generation are quantified.
  • The findings highlight a deeper connection between classical and quantum phenomena in stochastic processes.

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