Local Limits of One-Sided Trees

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Standard

Local Limits of One-Sided Trees. / Durhuus, Bergfinnur; Ünel, Meltem.

I: La Matematica, 2024.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Durhuus, B & Ünel, M 2024, 'Local Limits of One-Sided Trees', La Matematica. https://doi.org/10.1007/s44007-023-00080-z

APA

Durhuus, B., & Ünel, M. (2024). Local Limits of One-Sided Trees. La Matematica. https://doi.org/10.1007/s44007-023-00080-z

Vancouver

Durhuus B, Ünel M. Local Limits of One-Sided Trees. La Matematica. 2024. https://doi.org/10.1007/s44007-023-00080-z

Author

Durhuus, Bergfinnur ; Ünel, Meltem. / Local Limits of One-Sided Trees. I: La Matematica. 2024.

Bibtex

@article{419d6347327a405d81ba1e66412d1f4a,
title = "Local Limits of One-Sided Trees",
abstract = "A finite one-sided tree of height h is defined as a rooted planar tree obtained by grafting branches on one side, say the right, of a spine, i.e. a linear path of length h starting at the root, such that the resulting tree has no simple path starting at the root of length greater than h. We consider the distribution on the set of one-sided trees T of fixed size N, such that the weight of T is proportional to , where is a real constant and h(T) denotes the height of T. We show that, for N large, has a weak limit as a probability measure supported on infinite one-sided trees. The dependence of the limit measure on shows a transition at from a single-spine phase for to a multi-spine phase for . Correspondingly, there is a transition in the volume growth rate of balls around the root as a function of radius from linear growth for , to quadratic growth at , and to cubic growth for .",
author = "Bergfinnur Durhuus and Meltem {\"U}nel",
year = "2024",
doi = "10.1007/s44007-023-00080-z",
language = "English",
journal = "La Matematica",
issn = "2730-9657",

}

RIS

TY - JOUR

T1 - Local Limits of One-Sided Trees

AU - Durhuus, Bergfinnur

AU - Ünel, Meltem

PY - 2024

Y1 - 2024

N2 - A finite one-sided tree of height h is defined as a rooted planar tree obtained by grafting branches on one side, say the right, of a spine, i.e. a linear path of length h starting at the root, such that the resulting tree has no simple path starting at the root of length greater than h. We consider the distribution on the set of one-sided trees T of fixed size N, such that the weight of T is proportional to , where is a real constant and h(T) denotes the height of T. We show that, for N large, has a weak limit as a probability measure supported on infinite one-sided trees. The dependence of the limit measure on shows a transition at from a single-spine phase for to a multi-spine phase for . Correspondingly, there is a transition in the volume growth rate of balls around the root as a function of radius from linear growth for , to quadratic growth at , and to cubic growth for .

AB - A finite one-sided tree of height h is defined as a rooted planar tree obtained by grafting branches on one side, say the right, of a spine, i.e. a linear path of length h starting at the root, such that the resulting tree has no simple path starting at the root of length greater than h. We consider the distribution on the set of one-sided trees T of fixed size N, such that the weight of T is proportional to , where is a real constant and h(T) denotes the height of T. We show that, for N large, has a weak limit as a probability measure supported on infinite one-sided trees. The dependence of the limit measure on shows a transition at from a single-spine phase for to a multi-spine phase for . Correspondingly, there is a transition in the volume growth rate of balls around the root as a function of radius from linear growth for , to quadratic growth at , and to cubic growth for .

U2 - 10.1007/s44007-023-00080-z

DO - 10.1007/s44007-023-00080-z

M3 - Journal article

JO - La Matematica

JF - La Matematica

SN - 2730-9657

ER -

ID: 377442199