Minimal growth harmonic functions on lamplighter groups

Itai Benjamini; Hugo Duminil-Copin; Gady Kozma; Ariel Yadin

Minimal growth harmonic functions on lamplighter groups

Itai Benjamini, Hugo Duminil-Copin, Gady Kozma, Ariel Yadin

Department of Mathematics

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

4 Scopus citations

Abstract

We study the minimal possible growth of harmonic functions on lamplighters. We find that (Z/2) (Formula presented.) Z² has no sublinear harmonic functions, (Z/2) (Formula presented.) Z² has no sublogarithmic harmonic functions, and neither has the repeated wreath product (… (Z/2 (Formula presented.) Z²) (Formula presented.) Z²) (Formula presented.) … (Symbol found) Z². These results have implications on attempts to quantify the Derriennic-Kaimanovich-Vershik theorem.

Original language	English
Pages (from-to)	833-858
Number of pages	26
Journal	New York Journal of Mathematics
Volume	23
State	Published - 16 Jul 2017

Keywords

Entropy
Harmonic functions
Kaimanovich-Vershik
Lamplighter
Random walk
Wreath product

ASJC Scopus subject areas

General Mathematics

Cite this

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title = "Minimal growth harmonic functions on lamplighter groups",

abstract = "We study the minimal possible growth of harmonic functions on lamplighters. We find that (Z/2) (Formula presented.) Z2 has no sublinear harmonic functions, (Z/2) (Formula presented.) Z2 has no sublogarithmic harmonic functions, and neither has the repeated wreath product (… (Z/2 (Formula presented.) Z2) (Formula presented.) Z2) (Formula presented.) … (Symbol found) Z2. These results have implications on attempts to quantify the Derriennic-Kaimanovich-Vershik theorem.",

keywords = "Entropy, Harmonic functions, Kaimanovich-Vershik, Lamplighter, Random walk, Wreath product",

author = "Itai Benjamini and Hugo Duminil-Copin and Gady Kozma and Ariel Yadin",

year = "2017",

month = jul,

day = "16",

language = "English",

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pages = "833--858",

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T1 - Minimal growth harmonic functions on lamplighter groups

AU - Benjamini, Itai

AU - Duminil-Copin, Hugo

AU - Kozma, Gady

AU - Yadin, Ariel

PY - 2017/7/16

Y1 - 2017/7/16

N2 - We study the minimal possible growth of harmonic functions on lamplighters. We find that (Z/2) (Formula presented.) Z2 has no sublinear harmonic functions, (Z/2) (Formula presented.) Z2 has no sublogarithmic harmonic functions, and neither has the repeated wreath product (… (Z/2 (Formula presented.) Z2) (Formula presented.) Z2) (Formula presented.) … (Symbol found) Z2. These results have implications on attempts to quantify the Derriennic-Kaimanovich-Vershik theorem.

AB - We study the minimal possible growth of harmonic functions on lamplighters. We find that (Z/2) (Formula presented.) Z2 has no sublinear harmonic functions, (Z/2) (Formula presented.) Z2 has no sublogarithmic harmonic functions, and neither has the repeated wreath product (… (Z/2 (Formula presented.) Z2) (Formula presented.) Z2) (Formula presented.) … (Symbol found) Z2. These results have implications on attempts to quantify the Derriennic-Kaimanovich-Vershik theorem.

KW - Entropy

KW - Harmonic functions

KW - Kaimanovich-Vershik

KW - Lamplighter

KW - Random walk

KW - Wreath product

UR - http://www.scopus.com/inward/record.url?scp=85026781609&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85026781609

SN - 1076-9803

VL - 23

SP - 833

EP - 858

JO - New York Journal of Mathematics

JF - New York Journal of Mathematics

ER -

Minimal growth harmonic functions on lamplighter groups

Abstract

Keywords

ASJC Scopus subject areas

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