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Let T be a rooted multi-type Galton-Watson (MGW) tree of finitely many types with at least one offspring at each vertex, and an offspring distribution with exponential tails. The lambda-biased random...
This note presents some central limit theorems for the eigenvalue counting function of Wigner matrices in the form of suitable translations of results by Gustavsson and O'Rourke on the limiting behavi...
In this article, we show that Kerov’s central limit theorem related to the fluctuations of Young diagrams under the Plancherel measure extends to the case of Schur-Weyl measures, which are the probab...
We introduce a simple instance of the renormalization group transformation in the Banach space of probability densities. By changing the scaling of the renormalized variables we obtain, as fixed point...
In Dolera, Gabetta and Regazzini [Ann. Appl. Probab. 19 (2009)186–201] it is proved that the total variation distance between the solution f(·, t) of Kac’s equation and the Gaussian density (0,2) has...

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