Abstract
AbstractWe prove that the rescaled historical processes associated to critical spread-out lattice trees in dimensions $$d>8$$
d
>
8
converge to historical Brownian motion. This is a functional limit theorem for measure-valued processes that encodes the genealogical structure of the underlying random trees. Our results are applied elsewhere to prove that random walks on lattice trees, appropriately rescaled, converge to Brownian motion on super-Brownian motion.
Funder
Canadian Network for Research and Innovation in Machining Technology, Natural Sciences and Engineering Research Council of Canada
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Statistical and Nonlinear Physics
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