3 papers
math.GR2019
Polynomially growing harmonic functions on connected groups
Idan Perl, Ariel Yadin
We study the connection between the dimension of certain spaces of harmonic functions on a group and its geometric and algebraic properties. Our main result shows that (for suffici…
math.PR2018
SIT measures and Transience
Idan Perl
A graph is called (edge)-SIT if for some probability measure on paths, the number of mutual edges in two independent paths has finite mean. We show that transience is equivalent to…
math.GR2017
Harmonic functions on locally compact groups of polynomial growth
Idan Perl, Maud Szusterman
We extend a theorem by Kleiner, stating that on a group with polynomial growth, the space of harmonic functions of polynomial of at most is finite dimensional, to the settings…