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Universal Framework for Record Ages under Restart.

Aanjaneya Kumar1, Arnab Pal2,3

  • 1Department of Physics, Indian Institute of Science Education and Research, Dr. Homi Bhabha Road, Pune 411008, India.

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|April 28, 2023
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Summary
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We developed a universal framework to analyze record age statistics in stochastic time series with random restarts. Our findings reveal a penalty on record creation due to restarts, impacting complex systems analysis.

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Area of Science:

  • Statistical Physics
  • Complex Systems Analysis
  • Stochastic Processes

Background:

  • Record age statistics are crucial for understanding time series dynamics.
  • Random restarts are common in various complex systems, altering their behavior.
  • Existing models often assume Markovian processes, limiting applicability.

Purpose of the Study:

  • To propose a universal framework for computing record age statistics in stochastic time series with random restarts.
  • To analyze the impact of generic restart protocols, including non-Markovian settings.
  • To provide a tool for studying complex systems with restart mechanisms.

Main Methods:

  • Developed a universal computational framework for record age statistics.
  • Benchmarked the framework using classical random walks on a 1D lattice.
  • Derived a universal criterion for the impact of restarts on nth record age for nearest-neighbor transitions.

Main Results:

  • The framework is applicable to generic restart protocols beyond the Markovian setting.
  • A universal criterion reveals a penalty of order n on record creation due to restarts.
  • Demonstrated applicability on an aggregation-shattering process, computing typical growth rates.

Conclusions:

  • The proposed framework offers a unified approach to studying time series under restart.
  • Restarting mechanisms can significantly constrain, rather than expedite, record creation.
  • This work opens avenues for exploring record statistics in diverse complex systems.