Fluctuations of the Gromov-Prohorov sample model

2 Dec 2019 Jacques de Catelan Pierre-Loïc Méliot

In this paper, we study the fluctuations of observables of metric measure spaces which are random discrete approximations $X_n$ of a fixed arbitrary (complete, separable) metric measure space $X=(\mathcal{X},d,\mu)$. These observables $\Phi(X_n)$ are polynomials in the sense of Greven-Pfaffelhuber-Winter, and we show that for a generic model space $X$, they yield asymptotically normal random variables... (read more)

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