Displaying similar documents to “Regularity of formation of dust in self-similar fragmentations”

Strong law of large numbers for fragmentation processes

S. C. Harris, R. Knobloch, A. E. Kyprianou (2010)

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

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In the spirit of a classical result for Crump–Mode–Jagers processes, we prove a strong law of large numbers for fragmentation processes. Specifically, for self-similar fragmentation processes, including homogenous processes, we prove the almost sure convergence of an empirical measure associated with the stopping line corresponding to first fragments of size strictly smaller than for 1≥>0.

Quenched non-equilibrium central limit theorem for a tagged particle in the exclusion process with bond disorder

M. D. Jara, C. Landim (2008)

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

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For a sequence of i.i.d. random variables { : ∈ℤ} bounded above and below by strictly positive finite constants, consider the nearest-neighbor one-dimensional simple exclusion process in which a particle at (resp. +1) jumps to +1 (resp. ) at rate . We examine a quenched non-equilibrium central limit theorem for the position of a tagged particle in the exclusion process with bond disorder { : ∈ℤ}. We prove that the position of the tagged...