The fixed points of branching Brownian motion

Xinxin Chen (1, 2) , Christophe Garban (2, 3, 1) , Atul Shekhar (2, 1)

1 PSPM - Probabilités, statistique, physique mathématique
2 ICJ - Institut Camille Jordan
3 IUF - Institut universitaire de France

In this work, we characterize all the point processes θ = i∈N δx i on R which are left invariant under branching Brownian motions with critical drift − √ 2. Our characterization holds under the only assumption that θ is locally finite and θ(R +) < ∞ almost surely.

Mots clés: Branching Brownian motion; infinite particle system; invariant measures; decorated Poisson point process. Mathematics Subject Classification: 60G55; 60J80

Domaines: Probabilités [math.PR]

Xinxin Chen, Christophe Garban, Atul Shekhar. The fixed points of branching Brownian motion. Probability Theory and Related Fields, 2022, 185, pp.839-884. ⟨10.1007/s00440-022-01183-4⟩. ⟨hal-03774720⟩