Groups with minimal harmonic functions as small as you like (With an appendix by Nicolas Matte Bon)

Gideon Amir; Gady Kozma

Groups with minimal harmonic functions as small as you like (With an appendix by Nicolas Matte Bon)

Group Theory 2017-02-07 v2 Probability

Authors: Gideon Amir , Gady Kozma

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 in which the base group is defined via its properly chosen Schreier graph.

Keywords

harmonic functions growth order finitely-generated group Cayley graph permutational wreath products Schreier graph minimal growth

Cite

@article{arxiv.1605.07593,
  title  = {Groups with minimal harmonic functions as small as you like (With an appendix by Nicolas Matte Bon)},
  author = {Gideon Amir and Gady Kozma},
  journal= {arXiv preprint arXiv:1605.07593},
  year   = {2017}
}

Comments

20+7 pages, 4 figures. This version includes an appendix by Nicolas Matte Bon

Groups with minimal harmonic functions as small as you like (With an appendix by Nicolas Matte Bon)

Abstract

Keywords

Cite

Comments

Related papers