Abstracts of the Talks

S OF THE TALKS Hillel Furstenberg, Hebrew U. Qualitative Laws of Large Numbers. Abstract: If X1,X2, . . . ,Xn, . . . is an iid sequence of non-singular matrices, and we form the ”random product” Yn = X1 ∗ X2 ∗ X3 ∗ ⋯ ∗ Xn and let n → ∞ we find that the Yn tend to have a certain form. We analyze this phenomenon. If X1,X2, . . . ,Xn, . . . is an iid sequence of non-singular matrices, and we form the ”random product” Yn = X1 ∗ X2 ∗ X3 ∗ ⋯ ∗ Xn and let n → ∞ we find that the Yn tend to have a certain form. We analyze this phenomenon. Alexander Kachurovskii, Sobolev Inst. Maths Rates of convergence in ergodic theorems The talk is based on the joint survey with my student Ivan Podvigin. Abstract: The estimates of the rates of convergence will be given in the talk: in von Neumann’s ergodic theorem via the rate of correlations decay, and via the singularity at zero of the spectral measure of the function being averaged with respect to the corresponding dynamical system; in Birkhoff’s ergodic theorem via convergence rate in von Neumann’s ergodic theorem, and via large deviations rate of decay. The reasons of naturalness of obtaining these very estimates, are discussed. Estimates of convergence rates in both ergodic theorems are given for important in applications classes of dynamical systems, including some well-known billiards and Anosov systems. The estimates of the rates of convergence will be given in the talk: in von Neumann’s ergodic theorem via the rate of correlations decay, and via the singularity at zero of the spectral measure of the function being averaged with respect to the corresponding dynamical system; in Birkhoff’s ergodic theorem via convergence rate in von Neumann’s ergodic theorem, and via large deviations rate of decay. The reasons of naturalness of obtaining these very estimates, are discussed. Estimates of convergence rates in both ergodic theorems are given for important in applications classes of dynamical systems, including some well-known billiards and Anosov systems. Vadim Kaimanovich, U of Ottawa Boundary actions of random subgroups Joint work with Jan Cannizzo. Abstract: One of the most basic questions one can ask about a general measure class preserving action of a countable group is that about its conservativity vs. dissipativity (i.e., absence or presence of non-trivial wandering sets). If one looks at the action of a subgroup on the boundary of an ambient group, then for general subgroups this action may well be One of the most basic questions one can ask about a general measure class preserving action of a countable group is that about its conservativity vs. dissipativity (i.e., absence or presence of non-trivial wandering sets). If one looks at the action of a subgroup on the boundary of an ambient group, then for general subgroups this action may well be