Stochastic approximation of lamplighter metrics

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F22%3A00363345" target="_blank" >RIV/68407700:21230/22:00363345 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.1112/blms.12657" target="_blank" >https://doi.org/10.1112/blms.12657</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1112/blms.12657" target="_blank" >10.1112/blms.12657</a>

Result language

angličtina

Original language name

Stochastic approximation of lamplighter metrics

Original language description

We observe that embeddings into random metrics can be fruitfully used to study the L-1-embeddability of lamplighter graphs or groups, and more generally lamplighter metric spaces. Once this connection has been established, several new upper bound estimates on the L-1-distortion of lamplighter metrics follow from known related estimates about stochastic embeddings into dominating tree-metrics. For instance, every lamplighter metric on an n-point metric space embeds bi-Lipschitzly into L-1 with distortion O(logn). In particular, for every finite group G the lamplighter group H=Z(2) gimel G bi-Lipschitzly embeds into L-1 with distortion O(loglog|H|). In the case where the ground space in the lamplighter construction is a graph with some topological restrictions, better distortion estimates can be achieved. Finally, we discuss how a coarse embedding into L-1 of the lamplighter group over the d-dimensional infinite lattice Z(d) can be constructed from bi-Lipschitz embeddings of the lamplighter graphs over finite d-dimensional grids, and we include a remark on Lipschitz free spaces over finite metric spaces.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10101 - Pure mathematics

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2022

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Bulletin of the London Mathematical Society

ISSN

0024-6093

e-ISSN

1469-2120

Volume of the periodical

54

Issue of the periodical within the volume

5

Country of publishing house

GB - UNITED KINGDOM

Number of pages

23

Pages from-to

1804-1826

UT code for WoS article

000787367900001

EID of the result in the Scopus database

2-s2.0-85128812683