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First-passage and extreme value statistics for overdamped Brownian motion in a linear potential

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  • Huang, Feng
  • Chen, Hanshuang

Abstract

We investigate the first-passage properties and extreme-value statistics of an overdamped Brownian particle confined by an external linear potential V(x)=μ|x−x0|, where μ>0 is the strength of the potential and x0>0 is the position of the lowest point of the potential, which coincides with the starting position of the particle. The Brownian motion terminates whenever the particle passes through the origin at a random time tf. Our study reveals that the mean first-passage time 〈tf〉 exhibits a nonmonotonic behavior with respect to μ, with a unique minimum occurring at an optimal value of μ≃1.24468D/x0, where D is the diffusion constant of the Brownian particle. Moreover, we examine the distribution P(M|x0) of the maximum displacement M during the first-passage process, as well as the statistics of the time tm at which M is reached. Intriguingly, there exists another optimal μ≃1.24011D/x0 that minimizes the mean time 〈tm〉. All our analytical findings are corroborated through numerical simulations.

Suggested Citation

  • Huang, Feng & Chen, Hanshuang, 2025. "First-passage and extreme value statistics for overdamped Brownian motion in a linear potential," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 672(C).
    • Handle: RePEc:eee:phsmap:v:672:y:2025:i:c:s0378437125003255
    DOI: 10.1016/j.physa.2025.130673
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