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Large Deviations for Continuous Time Random Walks.

Wanli Wang1,2, Eli Barkai1,2, Stanislav Burov1

  • 1Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel.

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|December 8, 2020
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Summary
This summary is machine-generated.

Particle spreading in complex systems exhibits exponential decay, not Gaussian. Continuous time random walk models explain this, influenced by jump event timing like bunching and anti-bunching.

Keywords:
continuous time random walkdiffusing diffusivitylarge deviationsrenewal processsaddle point approximation

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Complex Systems

Background:

  • Particle spreading in complex environments often deviates from standard Gaussian models.
  • Recent observations show spatial exponential decay in particle movement tails within cellular and glassy systems.

Purpose of the Study:

  • To investigate the large deviation description of particle spreading using the continuous time random walk model.
  • To analyze how factors like jump event bunching and anti-bunching influence spatial decay patterns.

Main Methods:

  • Utilizing the continuous time random walk (CTRW) model.
  • Deriving the large deviation description for the particle propagator.
  • Analyzing exact solutions of the CTRW model to validate theoretical predictions.

Main Results:

  • Particle spreading follows an exponential decay with a logarithmic correction at large distances, under specific conditions on jump lengths and waiting times.
  • Anti-bunching of jump events reduces the exponential decay effect.
  • Bunching and intermittency of jump events enhance the exponential decay.

Conclusions:

  • The CTRW model provides a framework for understanding non-Gaussian particle spreading in complex systems.
  • The dynamics of jump events significantly modulate the spatial decay of particle distributions.
  • Theoretical predictions align with exact solutions, confirming the large deviation theory for these systems.