Journal article
Backbone scaling for critical lattice trees in high dimensions
Mark Holmes
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL | IOP PUBLISHING LTD | Published : 2016
Abstract
We prove that for critical (spread-out) lattice trees in dimensions d > 8, the unique paths from the origin to vertices of large tree distance converge to Brownian motion. This provides an important ingredient for proving weak convergence of the corresponding historical processes.
Grants
Funding Acknowledgements
This work was supported in part by a Marsden grant, administered by RSNZ. The author thanks two referees for helpful comments that led to significant improvements in the manuscript. The author also thanks Remco van der Hofstad and Ed Perkins for helpful discussions.