It is known (Hofmann-Credner and Stolz (2008) [4]) that the convergence of the mean empirical spectral distribution of a sample covariance matrix Wn=1/nYnYnt to the Marčenko–Pastur law remains unaffected if the rows and columns of Yn exhibit some dependence, where only the growth of the...

A crucial ingredient in social interaction models is the structure of peer groups with which individuals interact. We argue that this structure can vary from one individual to another and thus should be modeled as randomly distributed across individuals. We propose and study a dynamic binary...

A crucial ingredient in social interaction models is the structure of peer groups, which link individuals with similar characteristics. We propose and study a dynamic binary choice model with social interactions in which heterogeneity of peer group effects is modeled introducing diversity in...

The so-called swapping algorithm was designed to simulate from spin glass distributions, among others. In this note we show that it mixes rapidly, in a very simple disordered system, the Hopfield model with two patterns.

We define a Potts version of neural networks with q states. We give upper and lower bounds for the storage capacity of this model of associative memory in the sense of exact retrieval of the stored information. The critical capacity is of the order where N is the number of neurons and the...

This note relates the storage capacity of the Hopfield model of neural networks with possibly correlated patterns to a moderate deviation upper bound for the empirical correlation of the patterns. Examples are, among others, independent patterns with spins that are correlated as in an Ising...