Join sizes, urn models and normal limiting distributions

Limiting Distributions for a Class of Diminishing Urn Models

In this work we analyze a class of 2× 2 Pólya-Eggenberger urn models with ball replacement matrix M = (−a 0 c −d ) , a, d ∈ N, and c = p · a with p ∈ N0. We obtain limiting distributions for this 2 × 2 urn model by obtaining a precise recursive description of the moments of the considered random variables, which allows us to deduce asymptotic expansions of the moments. In particular, we obtain ...

Join distributions of synchronization models

We consider Markov models of multicomponent systems with synchronizing interaction. Under natural regularity assumptions about the message routing graph, they have nice longtime behavior. We are interested in limit probability laws related to the steady state viewed from the center-of-mass coordinate system.

Limiting Conditional Distributions for Stochastic Metapopulation Models

We consider a Markovian model proposed by Gyllenberg and Silvestrov [5] for studying the behaviour of a metapopulation: a population that occupies several geographically separated habitat patches. Although the individual patches may become empty through extinction of local populations, they can be recolonized through migration from other patches. There is considerable empirical evidence (see fo...

Join Sizes, Frequency Moments, and Applications

Dynamic Models for File Sizes and Double Pareto Distributions

In this paper, we introduce and analyze a new generative user model to explain the behavior of file size distributions. Our Recursive Forest File model combines ideas from recent work by Downey with ideas from recent work on random graph models for the Web. Unlike similar previous work, our Recursive Forest File model allows new files to be created and old files to be deleted over time, and our...