Displaying similar documents to “Random networks with sublinear preferential attachment: degree evolutions.”

Shao's theorem on the maximum of standardized random walk increments for multidimensional arrays

Zakhar Kabluchko, Axel Munk (2009)

ESAIM: Probability and Statistics

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We generalize a theorem of Shao [ (1995) 575–582] on the almost-sure limiting behavior of the maximum of standardized random walk increments to multidimensional arrays of i.i.d. random variables. The main difficulty is the absence of an appropriate strong approximation result in the multidimensional setting. The multiscale statistic under consideration was used recently for the selection of the regularization parameter in a number of statistical algorithms as well...

Ageing in the parabolic Anderson model

Peter Mörters, Marcel Ortgiese, Nadia Sidorova (2011)

Annales de l'I.H.P. Probabilités et statistiques

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The parabolic Anderson model is the Cauchy problem for the heat equation with a random potential. We consider this model in a setting which is continuous in time and discrete in space, and focus on time-constant, independent and identically distributed potentials with polynomial tails at infinity. We are concerned with the long-term temporal dynamics of this system. Our main result is that the periods, in which the profile of the solutions remains nearly constant, are increasing linearly...