Manfred Denker: Ergodic averages of multivariate functions

Let $(X,m,T)$ be a probability preserving transformation. For a multivariate function $h(x_1,...,x_d)$ I will discuss convergence properties of averages
$$ \frac 1{n^d} \sum_{1\le i_1,...,i_d\ne n} h(T^{i_1}(x),..., T^{i_d}(x))$$
from the dynamical and ergodic theoretical viewpoints: $h$ may be defined as a function or as an element in some tensor product. In the latter case I will discuss recent results with M. Gordin on the extension of the ergodic theorem, the central limit theorem and the convergence theorem towards generalized $\chi^2$ distributions.