Balázs Szegedy: Cubic excangeability and additive limits

Speaker: Balázs Szegedy

Title: Cubic excangeability and additive limits

Abstract: We present a new exchangeability result for random variables that are indexed by the vertices of the infinite dimensional cube. We assume that for every natural number k the marginals on affine k dimensional sub-cubes are all the same. We give a complete characterization of such joint distributions in terms of the recently developed theory of nilspaces. As a consequence, we obtain a structural limit theory for additive structures. Our result gives a new perspective on higher order Fourier analysis. Joint work with Pablo Candela.