Minimal growth harmonic functions on lamplighter groups

被引：0

作者：

Benjamini, Itai ^{[1
]}

Duminil-Copin, Hugo ^{[2
,3
]}

Kozma, Gady ^{[1
]}

Yadin, Ariel ^{[4
]}

机构：

[1] Weizmann Inst Sci, Rehovot, Israel

[2] Inst Hautes Etud Sci, Bures Sur Yvette, France

[3] Univ Geneva, Geneva, Switzerland

[4] Ben Gurion Univ Negev, Beer Sheva, Israel

来源：

NEW YORK JOURNAL OF MATHEMATICS | 2017年 / 23卷

关键词：

Harmonic functions; random walk; lamplighter; wreath product; entropy; Kaimanovich-Vershik; POLYNOMIAL VOLUME GROWTH; RANDOM-WALKS; GRAPHS;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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

引用

页码：833 / 858

页数：26

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