We consider a variant of the randomly reinforced urn where more balls can be simultaneously drawn out and balls of different colors can be simultaneously added. More precisely, at each time-step, the conditional distribution of the number of extracte
d balls of a certain color given the past is assumed to be hypergeometric. We prove some central limit theorems in the sense of stable convergence and of almost sure conditional convergence, which are stronger than convergence in distribution. The proven results provide asymptotic confidence intervals for the limit proportion, whose distribution is generally unknown. Moreover, we also consider the case of more urns subjected to some random common factors.
The quest for a model that is able to explain, describe, analyze and simulate real-world complex networks is of uttermost practical as well as theoretical interest. In this paper we introduce and study a network model that is based on a latent attrib
ute structure: each node is characterized by a number of features and the probability of the existence of an edge between two nodes depends on the features they share. Features are chosen according to a process of Indian-Buffet type but with an additional random fitness parameter attached to each node, that determines its ability to transmit its own features to other nodes. As a consequence, a nodes connectivity does not depend on its age alone, so also young nodes are able to compete and succeed in acquiring links. One of the advantages of our model for the latent bipartite node-attribute network is that it depends on few parameters with a straightforward interpretation. We provide some theoretical, as well experimental, results regarding the power-law behaviour of the model and the estimation of the parameters. By experimental data, we also show how the proposed model for the attribute structure naturally captures most local and global properties (e.g., degree distributions, connectivity and distance distributions) real networks exhibit. keyword: Complex network, social network, attribute matrix, Indian Buffet process
Let (X_n) be a sequence of random variables (with values in a separable metric space) and (N_n) a sequence of random indices. Conditions for X_{N_n} to converge stably (in particular, in distribution) are provided. Some examples, where such condition
s work but those already existing fail, are given as well. Key words and phrases: Anscombe theorem, Exchangeability, Random indices, Random sums, Stable convergence
