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Inequalities and limit theorems for random allocations

István Fazekas, Alexey Chuprunov, József Túri (2011)

Annales UMCS, Mathematica

Random allocations of balls into boxes are considered. Properties of the number of boxes containing a fixed number of balls are studied. A moment inequality is obtained. A merge theorem with Poissonian accompanying laws is proved. It implies an almost sure limit theorem with a mixture of Poissonian laws as limiting distribution. Almost sure versions of the central limit theorem are obtained when the parameters are in the central domain.

Isotropic random walks on affine buildings

James Parkinson (2007)

Annales de l’institut Fourier

In this paper we apply techniques of spherical harmonic analysis to prove a local limit theorem, a rate of escape theorem, and a central limit theorem for isotropic random walks on arbitrary thick regular affine buildings of irreducible type. This generalises results of Cartwright and Woess where A ˜ n buildings are studied, Lindlbauer and Voit where A ˜ 2 buildings are studied, and Sawyer where homogeneous trees are studied (these are A ˜ 1 buildings).

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