From Spin Glasses to Branching Brownian Motion—and Back?

Abstract

I review recent work on the construction of the extremal process of branching Brownian motion. I place this in the context of spin glass theory and in particular the Generalised Random Energy models of Derrida and Gardner. The main emphasis is on a review of the construction of the extremal process of branching Brownian motion, done in collaboration with Louis-Pierre Arguin and Nicola Kistler (Commun Pure Appl Math 64(12):1647–1676, 2011; Ann Appl Probab 22(4):1693–1711, 2012; Probab Theory Relat Fields 157:535–574, 2013). I also present some more recent results on the variable speed Brownian motion, obtained with Lisa Hartung (Electron J Probab 19(18):1–28, 2014; Lat Am J Probab Math Stat 12:261–291, 2015).