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...

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...

We show a principle of large deviations for sums of random variables which themselve obey a principle of large deviations with speed an and rate function I. The new rate function is again given by I, whereas the speed increases by a factor n to an n.

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...

We analyze the simulated annealing algorithm with an energy function Ut that depends on time. Assuming some regularity conditions on Ut (especially that Ut does not change too quickly in time), and choosing a logarithmic cooling schedule for the algorithm, we derive bounds on the Radon-Nikodym...

We show that for sufficiently large knapsacks the associated Markov chain on the state space of the admissible packings of the knapsack is rapidly mixing. Our condition basically states that at least half of all items should fit into the knapsack. This is much weaker than the condition assumed...