Cargando…
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...
Autores principales: | , , , |
---|---|
Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Springer Berlin Heidelberg
2023
|
Materias: | |
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 |
_version_ | 1785061521763598336 |
---|---|
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. |
format | Online Article Text |
id | pubmed-10285026 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2023 |
publisher | Springer Berlin Heidelberg |
record_format | MEDLINE/PubMed |
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 |
work_keys_str_mv | AT cabezasmanuel historicallatticetrees AT friberghalexander historicallatticetrees AT holmesmark historicallatticetrees AT perkinsedwin historicallatticetrees |