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...

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...

Matzinger (Random Structure Algorithm 15 (1999a) 196) showed how to reconstruct almost every three color scenery, that is a coloring of the integers with three colors, by observing it along the path of a simple random walk, if this scenery is the outcome of an i.i.d. process. This reconstruction...

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 give a criterion to ensure convergence of non-reversible simulated annealing algorithms to the set of global minima of the target function U. We show, that such conditions only have to take into account the structure of the local minima of U. Moreover we give an example showing that in...

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...

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.