Variable speed branching Brownian motion 1. Extremal processes in the weak correlation regime

Abstract

We prove the convergence of the extremal processes for variable speed branching Brownian motions where the "speed functions", that describe the time-inhomogeneous variance, lie strictly below their concave hull and satisfy a certain weak regularity condition. These limiting objects are universal in the sense that they only depend on the slope of the speed function at $0$ and the final time $t$. The proof is based on previous results for two-speed BBM obtained in a recent paper of ours and uses Gaussian comparison arguments to extend these to the general case.

29 pages, 3 figures, revised version

References in corpus (3)

• Extreme local extrema of two-dimensional discrete Gaussian free field
• Slowdown for time inhomogeneous branching Brownian motion
• Constrained Brownian motion: Fluctuations away from circular and parabolic barriers

Cited by in corpus (7)

• Freezing and decorated Poisson point processes
• Derrida's random energy models. From spin glasses to the extremes of correlated random fields
• Maxima of branching random walks with piecewise constant variance
• Extremes of the 2d scale-inhomogeneous discrete Gaussian free field: Sub-leading order and exponential tails
• Anomalous spreading in reducible multitype branching Brownian motion
• From $1$ to $6$: a finer analysis of perturbed branching Brownian motion
• Second and third orders asymptotic expansions for the distribution of particles in a branching random walk with a random environment in time