Invariance principle for the maximal position process of branching Brownian motion in random environment (Q6164931)

The authors study the maximal position of branching Brownian motion in random spatial environment under quenched law and under annealed law assuming certain conditions on the environment. A spine decomposition is introduced and some basic properties are proved for the eigenvalues and eigenfunctions along with a strong law of large numbers and a central limit theorem for the spine process and the main results are proved using the spine decomposition and the long-time behaviour of the spine process.