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First-passage time for many-particle diffusion in space-time random environments.

Jacob B Hass1, Ivan Corwin2, Eric I Corwin1

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Summary
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Investigating many-particle diffusion reveals that the extreme first-passage time differs significantly between independent particles and those influenced by a common random field. This difference allows indirect measurement of the diffusion environment.

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Area of Science:

  • Statistical Physics
  • Complex Systems
  • Computational Science

Background:

  • Single-particle diffusion and first-passage time are well-studied.
  • Many-particle diffusion, common in physical systems, has been less explored regarding first-passage times.
  • Existing models for many-particle diffusion include independent random walkers and particles coupled to a common random forcing field.

Purpose of the Study:

  • To investigate and compare the first-passage time statistics of many-particle diffusion systems under different models.
  • To develop a theoretical framework for analyzing the impact of a random environment on extreme first-passage times.
  • To establish whether extreme first-passage time measurements can serve as indirect probes of the diffusion environment.

Main Methods:

  • Comparison of two many-particle diffusion models: independent random walkers versus particles in a common random forcing field.
  • Development of an asymptotic theoretical framework to separate environmental effects from trajectory-specific behaviors.
  • Validation through numerical simulations across a range of particle numbers (down to 100).

Main Results:

  • Single-particle first-passage time statistics are similar across both models.
  • Extreme first-passage times for many particles diverge significantly between the two models due to the common forcing field.
  • A power law is identified that quantifies the environment's impact on the variance of the extreme first-passage time.

Conclusions:

  • The extreme first-passage time in many-particle diffusion is highly sensitive to the nature of the underlying random environment.
  • The developed asymptotic theory accurately predicts simulation results, even for moderate numbers of particles.
  • Measurements of extreme first-passage time offer a novel method for indirectly characterizing the diffusion environment.