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Dynamics at the edge for independent diffusing particles.

Pierre Le Doussal1

  • 1Laboratoire de Physique de l'École Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, 75005 Paris, France.

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Summary
This summary is machine-generated.

This study analyzes the extreme behavior of many independent Brownian particles. We derive key probability distributions for particle positions and arrival times at the system

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Area of Science:

  • Statistical physics
  • Stochastic processes

Background:

  • Brownian motion is fundamental to modeling random processes.
  • Understanding outlier dynamics is crucial in various scientific fields.

Purpose of the Study:

  • To investigate the statistical properties of extreme positions of independent Brownian particles.
  • To derive multitime joint distributions for particle dynamics.

Main Methods:

  • Derivation of probability distributions using two distinct analytical methods.
  • Analysis of joint distributions for maximum and second maximum positions.
  • Examination of counting statistics at the system's edge.

Main Results:

  • Obtained multitime joint distributions for the rightmost particle's position.
  • Derived two-time joint distributions for maximum and second maximum positions.
  • Characterized the running maximum and arrival time distributions.

Conclusions:

  • The study provides a comprehensive statistical description of Brownian particle outliers.
  • Derived distributions offer insights into the extreme dynamics of stochastic systems.