Historical Lattice Trees

We prove that the rescaled historical processes associated to critical spread-out lattice trees in dimensions [Formula: see text] converge to historical Brownian motion. This is a functional limit theorem for measure-valued processes that encodes the genealogical structure of the underlying random t...

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Autores principales: Cabezas, Manuel, Fribergh, Alexander, Holmes, Mark, Perkins, Edwin
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2023
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10285026/
https://www.ncbi.nlm.nih.gov/pubmed/37360187
http://dx.doi.org/10.1007/s00220-023-04641-9
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author Cabezas, Manuel
Fribergh, Alexander
Holmes, Mark
Perkins, Edwin
author_facet Cabezas, Manuel
Fribergh, Alexander
Holmes, Mark
Perkins, Edwin
author_sort Cabezas, Manuel
collection PubMed
description We prove that the rescaled historical processes associated to critical spread-out lattice trees in dimensions [Formula: see text] 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.
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spelling pubmed-102850262023-06-23 Historical Lattice Trees Cabezas, Manuel Fribergh, Alexander Holmes, Mark Perkins, Edwin Commun Math Phys Article We prove that the rescaled historical processes associated to critical spread-out lattice trees in dimensions [Formula: see text] 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. Springer Berlin Heidelberg 2023-01-31 2023 /pmc/articles/PMC10285026/ /pubmed/37360187 http://dx.doi.org/10.1007/s00220-023-04641-9 Text en © The Author(s) 2023 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Cabezas, Manuel
Fribergh, Alexander
Holmes, Mark
Perkins, Edwin
Historical Lattice Trees
title Historical Lattice Trees
title_full Historical Lattice Trees
title_fullStr Historical Lattice Trees
title_full_unstemmed Historical Lattice Trees
title_short Historical Lattice Trees
title_sort historical lattice trees
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10285026/
https://www.ncbi.nlm.nih.gov/pubmed/37360187
http://dx.doi.org/10.1007/s00220-023-04641-9
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AT holmesmark historicallatticetrees
AT perkinsedwin historicallatticetrees

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