Speaker
Timothée Bénard, Université Sorbonne Paris-Nord
Abstract
Let mu be a probability measure on a nilpotent Lie group G, whose support generates a dense subgroup. Is every bounded mu-harmonic function constant? This question was raised by Furstenberg and Guivarc’h. The answer is affirmative when G is abelian (Choquet-Deny, 1960) and even step 2 (Guivarc’h, 1973). I will provide a complete answer, for nilpotent Lie groups and beyond. Joint work with Joshua Frisch.