Minimal growth harmonic functions on lamplighter groups

被引:0
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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
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.
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页码:833 / 858
页数:26
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