Eric Derbez - Generating functions and Integrated SuperBrownian Excursion ( ISE)

Using the lace expansion (first developed by Brydges and Spencer) as implemented by Hara and Slade, Derbez and Slade have recently proved that lattice trees (studied in statistical mechanics) converge in an appropriate scaling limit to a variant of super Brownian motion known as Integrated SuperBrownian Excursion ( ISE). The key to linking these two seemingly disconnected models is a rather simple looking generating function.