Joram Seminar: Lev Buhovski (Tel-Aviv University) - 0,01% Improvement of the Liouville property for discrete harmonic functions on Z^2.

Fri, 11/01/201911:45-12:45
Manchester Building (Hall 2), Hebrew University Jerusalem
Let u be a harmonic function on the plane. The Liouville theorem claims that if |u| is bounded on the whole plane, then u is identically constant. It appears that if u is a harmonic function on the lattice Z^2, and |u| < 1 on 99,99% of Z^2, then u is a constant function. Based on a joint work with A. Logunov, Eu. Malinnikova and M. Sodin.