Institut für Mathematik


Modul:   MAT760  Ergodic Theory and Dynamical Systems Seminar

Measure classification and (non)-escape of mass for horospherical actions on regular trees

Vortrag von Dr. Cagri Sert

Datum: 23.09.19   Zeit: 14.00 - 15.00   Raum: ETH HG G 43

Let T be a d-regular tree (d > 2), R < Aut(T) be a lattice and U < Aut(T) the stabilizer of some end on the boundary of T, that do not contain hyperbolic elements (horospherical subgroup). In a first part, we study U-invariant ergodic probability measures on Aut(T)/ R and prove an Hedlund theorem when R is geometrically finite. In a second part, given a closed transitive subgroup G < Aut(T) and lattice R < G, we study non-escape of mass phenomenon for the U-action on G/R and we construct examples of R with escape of mass for the U-action using subgaussian concentration inequalities. Finally, we make connections between the geometric diophantine behaviour of ends and the speed of equidistribution of dense U-orbits in the aforementioned Hedlund theorem. Joint work with Corina Ciobotaru and Vladimir Finkelshtein.