Cargando…
Periodic Lorentz gas with small scatterers
We prove limit laws for infinite horizon planar periodic Lorentz gases when, as time n tends to infinity, the scatterer size [Formula: see text] may also tend to zero simultaneously at a sufficiently slow pace. In particular we obtain a non-standard Central Limit Theorem as well as a Local Limit The...
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/PMC10169905/ https://www.ncbi.nlm.nih.gov/pubmed/37181495 http://dx.doi.org/10.1007/s00440-023-01197-6 |
_version_ | 1785039139015491584 |
---|---|
author | Bálint, Péter Bruin, Henk Terhesiu, Dalia |
author_facet | Bálint, Péter Bruin, Henk Terhesiu, Dalia |
author_sort | Bálint, Péter |
collection | PubMed |
description | We prove limit laws for infinite horizon planar periodic Lorentz gases when, as time n tends to infinity, the scatterer size [Formula: see text] may also tend to zero simultaneously at a sufficiently slow pace. In particular we obtain a non-standard Central Limit Theorem as well as a Local Limit Theorem for the displacement function. To the best of our knowledge, these are the first results on an intermediate case between the two well-studied regimes with superdiffusive [Formula: see text] scaling (i) for fixed infinite horizon configurations—letting first [Formula: see text] and then [Formula: see text] —studied e.g. by Szász and Varjú (J Stat Phys 129(1):59–80, 2007) and (ii) Boltzmann–Grad type situations—letting first [Formula: see text] and then [Formula: see text] —studied by Marklof and Tóth (Commun Math Phys 347(3):933–981, 2016) . |
format | Online Article Text |
id | pubmed-10169905 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2023 |
publisher | Springer Berlin Heidelberg |
record_format | MEDLINE/PubMed |
spelling | pubmed-101699052023-05-11 Periodic Lorentz gas with small scatterers Bálint, Péter Bruin, Henk Terhesiu, Dalia Probab Theory Relat Fields Article We prove limit laws for infinite horizon planar periodic Lorentz gases when, as time n tends to infinity, the scatterer size [Formula: see text] may also tend to zero simultaneously at a sufficiently slow pace. In particular we obtain a non-standard Central Limit Theorem as well as a Local Limit Theorem for the displacement function. To the best of our knowledge, these are the first results on an intermediate case between the two well-studied regimes with superdiffusive [Formula: see text] scaling (i) for fixed infinite horizon configurations—letting first [Formula: see text] and then [Formula: see text] —studied e.g. by Szász and Varjú (J Stat Phys 129(1):59–80, 2007) and (ii) Boltzmann–Grad type situations—letting first [Formula: see text] and then [Formula: see text] —studied by Marklof and Tóth (Commun Math Phys 347(3):933–981, 2016) . Springer Berlin Heidelberg 2023-03-15 2023 /pmc/articles/PMC10169905/ /pubmed/37181495 http://dx.doi.org/10.1007/s00440-023-01197-6 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 Bálint, Péter Bruin, Henk Terhesiu, Dalia Periodic Lorentz gas with small scatterers |
title | Periodic Lorentz gas with small scatterers |
title_full | Periodic Lorentz gas with small scatterers |
title_fullStr | Periodic Lorentz gas with small scatterers |
title_full_unstemmed | Periodic Lorentz gas with small scatterers |
title_short | Periodic Lorentz gas with small scatterers |
title_sort | periodic lorentz gas with small scatterers |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10169905/ https://www.ncbi.nlm.nih.gov/pubmed/37181495 http://dx.doi.org/10.1007/s00440-023-01197-6 |
work_keys_str_mv | AT balintpeter periodiclorentzgaswithsmallscatterers AT bruinhenk periodiclorentzgaswithsmallscatterers AT terhesiudalia periodiclorentzgaswithsmallscatterers |