Scaling limits for simple random walks on random ordered graph trees

Content Provider	Semantic Scholar
Author	Croydon, David A.
Copyright Year	2010
Abstract	Consider a family of random ordered graph trees (T-n)(n >= 1), where T-n has n vertices. It has previously been established that if the associated search-depth processes converge to the normalised Brownian excursion when rescaled appropriately as n -> infinity, then the simple random walks on the graph trees have the Brownian motion on the Brownian continuum random tree as their scaling limit. Here, this result is extended to demonstrate the existence of a diffusion scaling limit whenever the volume measure on the limiting real tree is nonatomic, supported on the leaves of the limiting tree, and satisfies a polynomial lower bound for the volume of balls. Furthermore, as an application of this generalisation, it is established that the simple random walks on a family of Galton-Watson trees with a critical infinite variance offspring distribution, conditioned on the total number of offspring, can be resealed to converge to the Brownian motion on a related alpha-stable tree.
Starting Page	528
Ending Page	558
Page Count	31
File Format	PDF HTM / HTML
DOI	10.1239/aap/1275055241
Volume Number	42
Alternate Webpage(s)	https://www.cambridge.org/core/services/aop-cambridge-core/content/view/3DE2B96194B2486EE215828D68B975E4/S0001867800004183a.pdf/scaling_limits_for_simple_random_walks_on_random_ordered_graph_trees.pdf
Alternate Webpage(s)	https://arxiv.org/pdf/1210.5866v2.pdf
Alternate Webpage(s)	https://doi.org/10.1239/aap%2F1275055241
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article