English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We derive asymptotic formulas for the mean exit time $\bar{\tau}^{N}$ of thefastest among $N$ identical independently distributed Brownian particles to anabsorbing boundary for various initial distributions (partially uniformly andexponentially distributed). Depending on the tail of the initial distribution,we report here a continuous algebraic decay law for $\bar{\tau}^{N}$, whichdiffers from the classical Weibull or Gumbell results. We derive asymptoticformulas in dimension 1 and 2, for half-line and an interval that we comparewith stochastic simulations. We also obtain formulas for an additive constantdrift on the Brownian motion. Finally, we discuss some applications in cellbiology where a molecular transduction pathway involves multiple steps and along-tail initial distribution.

Asymptotics for the fastest among n stochastics particles: role of an extended initial distribution and an additional drift component