Stationary gap distributions for infinite systems of competing brownian particles

Andrey Sarantsev, Li Cheng Tsai

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


Consider the infinite Atlas model: a semi-infinite collection of particles driven by independent standard Brownian motions with zero drifts, except for the bottom-ranked particle which receives unit drift. We derive a continuum one-parameter family of product-of-exponentials stationary gap distributions, with exponentially growing density at infinity. This result shows that there are infinitely many stationary gap distributions for the Atlas model, and hence resolves a conjecture of Pal and Pitman (2008) [PP08] in the negative. This result is further generalized for infinite systems of competing Brownian particles with generic rank-based drifts.

Original languageEnglish (US)
Article number56
JournalElectronic Journal of Probability
StatePublished - 2017
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Competing Brownian particles
  • Gap process
  • Infinite Atlas model
  • Stationary distribution


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