Skip to Main content Skip to Navigation
Journal articles

Genealogy of the extremal process of the branching random walk

Abstract : Let (T, V) be a branching random walk on the real line. The extremal process of the branching random walk is the point process of the position of particles at time n shifted by the position of the minimum. Madaule [Mad15] proved that this point process converges toward a shifted decorated Poisson point process. In this article we study the joint convergence of the extremal process with its genealogy informations. This result is then used to characterize the law of the decoration in the limiting process as well as to study the supercritical Gibbs measures of the branching random walk.
Document type :
Journal articles
Complete list of metadata

Cited literature [36 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01326628
Contributor : Bastien Mallein Connect in order to contact the contributor
Submitted on : Saturday, September 29, 2018 - 11:01:23 AM
Last modification on : Wednesday, November 17, 2021 - 12:27:06 PM
Long-term archiving on: : Monday, December 31, 2018 - 10:57:59 AM

File

genealogyOfTheExtremalProcess....
Files produced by the author(s)

Identifiers

Collections

Citation

Bastien Mallein. Genealogy of the extremal process of the branching random walk. ALEA : Latin American Journal of Probability and Mathematical Statistics, Instituto Nacional de Matemática Pura e Aplicada, 2018, 15 (2), ⟨10.30757/ALEA.v15-39⟩. ⟨hal-01326628v2⟩

Share

Metrics

Record views

299

Files downloads

927