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Order statistics for d-dimensional diffusion processes.

S B Yuste1, L Acedo, K Lindenberg

  • 1Departamento de Física, Universidad de Extremadura, E-06071 Badajoz, Spain. santos@unex.es

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 12, 2001
PubMed
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We analyzed the arrival times of multiple random walkers reaching a boundary. This study provides insights into the statistical behavior of first-passage times in various dimensions.

Area of Science:

  • Probability theory
  • Statistical physics
  • Stochastic processes

Background:

  • First-passage time problems are fundamental in analyzing the behavior of random processes.
  • Understanding the collective dynamics of multiple random walkers is crucial in fields like finance and biology.

Purpose of the Study:

  • To investigate the statistical properties of the ordered sequence of first-passage times for N random walkers.
  • To analyze how these properties vary with the number of walkers (N) and the dimensionality (d) of the Euclidean space.

Main Methods:

  • Simulations of N random walkers in d-dimensional Euclidean spaces.
  • Analysis of the probability distributions and correlations of ordered first-passage times.

Main Results:

Related Experiment Videos

  • The study presents detailed results for the ordered sequence of first-passage times.
  • The statistical distributions exhibit dependencies on N and d.

Conclusions:

  • The findings offer a comprehensive understanding of multi-particle first-passage time statistics.
  • This research contributes to the theoretical framework of stochastic processes in higher dimensions.