# Slow Kinetics of Brownian Maxima

Source: [Slow Kinetics of Brownian Maxima](<https://www.sota2.com/research/paper/68fa2d7b1e209131ce859b34>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T16:17:09.388Z

Authors: E. Ben-Naim, P.L. Krapivsky

Published: 2014-05-03T04:20:07.000Z

## Abstract

We study extreme-value statistics of Brownian trajectories in one dimension. We define the maximum as the largest position to date and compare maxima of two particles undergoing independent Brownian motion. We focus on the probability P(t) that the two maxima remain ordered up to time t, and find the algebraic decay P ~ t^(-beta) with exponent beta=1/4. When the two particles have diffusion constants D1 and D2, the exponent depends on the mobilities, beta=(1/pi)arctan\[sqrt(D2/D1)\]. We also use numerical simulations to investigate maxima of multiple particles in one dimension and the largest extension of particles in higher dimensions.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1405.0553>)

[PDF](<https://arxiv.org/pdf/1405.0553.pdf>)