Groups with minimal harmonic functions as small as you like

Gideon Amir; Gady Kozma; Nicolás Matte Bon

doi:10.4171/GGD/748

Groups with minimal harmonic functions as small as you like

Gideon Amir, Gady Kozma, Nicolás Matte Bon

Bar-Ilan University, Weizmann Institute of Science

Research output: Contribution to journal › Article › peer-review

Abstract

For any order of growth f (n) = o(log n), we construct a finitely-generated group G and a set of generators S such that the Cayley graph of G with respect to S supports a harmonic function with growth f but does not support any harmonic function with slower growth. The construction uses permutational wreath products Z/2 ≀_X Γ in which the base group Γ is defined via its properly chosen action on X .

Original language	English
Pages (from-to)	1-24
Number of pages	24
Journal	Groups, Geometry, and Dynamics
Volume	18
Issue number	1
DOIs	https://doi.org/10.4171/GGD/748
State	Published - 13 Feb 2024

Keywords

Harmonic functions
Schreier graphs
group actions
random walks

All Science Journal Classification (ASJC) codes

Geometry and Topology
Discrete Mathematics and Combinatorics

Access to Document

10.4171/GGD/748

Cite this

@article{9d1571a585344778ba41045bf53fbd6c,

title = "Groups with minimal harmonic functions as small as you like",

abstract = "For any order of growth f (n) = o(log n), we construct a finitely-generated group G and a set of generators S such that the Cayley graph of G with respect to S supports a harmonic function with growth f but does not support any harmonic function with slower growth. The construction uses permutational wreath products Z/2 ≀X Γ in which the base group Γ is defined via its properly chosen action on X .",

keywords = "Harmonic functions, Schreier graphs, group actions, random walks",

author = "Gideon Amir and Gady Kozma and Bon, {Nicol{\'a}s Matte}",

note = "Publisher Copyright: {\textcopyright} 2023 European Mathematical Society.",

year = "2024",

month = feb,

day = "13",

doi = "10.4171/GGD/748",

language = "الإنجليزيّة",

volume = "18",

pages = "1--24",

journal = "Groups, Geometry, and Dynamics",

issn = "1661-7207",

publisher = "European Mathematical Society Publishing House",

number = "1",

}

TY - JOUR

T1 - Groups with minimal harmonic functions as small as you like

AU - Amir, Gideon

AU - Kozma, Gady

AU - Bon, Nicolás Matte

PY - 2024/2/13

Y1 - 2024/2/13

N2 - For any order of growth f (n) = o(log n), we construct a finitely-generated group G and a set of generators S such that the Cayley graph of G with respect to S supports a harmonic function with growth f but does not support any harmonic function with slower growth. The construction uses permutational wreath products Z/2 ≀X Γ in which the base group Γ is defined via its properly chosen action on X .

AB - For any order of growth f (n) = o(log n), we construct a finitely-generated group G and a set of generators S such that the Cayley graph of G with respect to S supports a harmonic function with growth f but does not support any harmonic function with slower growth. The construction uses permutational wreath products Z/2 ≀X Γ in which the base group Γ is defined via its properly chosen action on X .

KW - Harmonic functions

KW - Schreier graphs

KW - group actions

KW - random walks

UR - http://www.scopus.com/inward/record.url?scp=85186464434&partnerID=8YFLogxK

U2 - 10.4171/GGD/748

DO - 10.4171/GGD/748

M3 - مقالة

SN - 1661-7207

VL - 18

SP - 1

EP - 24

JO - Groups, Geometry, and Dynamics

JF - Groups, Geometry, and Dynamics

IS - 1

ER -

Groups with minimal harmonic functions as small as you like

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this