Rigidity of infinite exchangeable sequences
In recent works, it has been shown that infinite exchangeable sequences with Gaussian marginals have remarkable rigidity properties, namely that Gaussianity of just the first two elements of the sequence implies the whole sequence is Gaussian. I will present the general case of mixture kernels and demonstrate that an analogous result holds, namely that the distribution of the first three elements of the sequence determines the full law of the sequence under a Muntz-Szasz type criterion. These results strengthen many results in non-parametric identifiability of mixtures and yield sharp finite-dimensional refinements of classical theorems of Schoenberg and Freedman.
Marcus Michelen
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