From 1 to 6: A Finer Analysis of Perturbed Branching Brownian Motion

From 1 to 6: A Finer Analysis of Perturbed Branching Brownian Motion

The logarithmic correction for the order of the maximum for two‐speed branching Brownian motion changes discontinuously when approaching slopes σ12=σ22=1, which corresponds to standard branching Brownian motion. In this article we study this transition more closely by choosing σ12=1±t−α and σ22=1∓t−...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Communications on pure and applied mathematics 2020-07, Vol.73 (7), p.1490-1525
Hauptverfasser: Bovier, Anton, Hartung, Lisa
Format: Artikel
Sprache:eng
Schlagworte:
Applications of mathematics
Brownian motion
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:The logarithmic correction for the order of the maximum for two‐speed branching Brownian motion changes discontinuously when approaching slopes σ12=σ22=1, which corresponds to standard branching Brownian motion. In this article we study this transition more closely by choosing σ12=1±t−α and σ22=1∓t−α. We show that the logarithmic correction for the order of the maximum now smoothly interpolates between the correction in the i.i.d. case 122lnt,322lnt, and 622lnt when 0
ISSN:0010-3640
1097-0312
DOI:10.1002/cpa.21893