Continuity estimates for the complex cascade model on the phase boundary

Thomas Madaule (1) , Rémi Rhodes (2) , Vincent Vargas (3)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
3 DMA - Département de Mathématiques et Applications - ENS Paris

We consider the complex branching random walk on a dyadic tree with Gaussian weights on the boundary between the diffuse phase and the glassy phase. We study the branching random walk in the space of continuous functions and establish convergence in this space. The main difficulty here is that the expected modulus of continuity of the limit is too weak in order to show tightness in the space of continuous functions by means of standard tools from the theory of stochastic processes.

Mots clés: branching random walk; complex weights; boundary case; diffusivity

Domaines: Probabilités [math.PR]

Thomas Madaule, Rémi Rhodes, Vincent Vargas. Continuity estimates for the complex cascade model on the phase boundary. 2015. ⟨hal-01161635⟩