Large deviations principle for Curie-Weiss models with random fields

In this article we consider an extension of the classical Curie-Weiss model in which the global and deterministic external magnetic field is replaced by local and random external fields which interact with each spin of the system. We prove a Large Deviations Principle for the so-called {\it magnetization per spin} $S_n/n$ with respect to the associated Gibbs measure, where $S_n/n$ is the scaled partial sum of spins. In particular, we obtain an explicit expression for the LDP rate function, which enables an extensive study of the phase diagram in some examples. It is worth mentioning that the model considered in this article covers, in particular, both the case of i.\,i.\,d.\ random external fields (also known under the name of random field Curie-Weiss models) and the case of dependent random external fields generated by e.\,g.\ Markov chains or dynamical systems.Comment: 11 page

Large deviations for disordered bosons and multiple orthogonal polynomial ensembles

We prove a large deviations principle for the empirical measures of a class of biorthogonal and multiple orthogonal polynomial ensembles that includes biorthogonal Laguerre, Jacobi and Hermite ensembles, the matrix model of Lueck, Sommers and Zirnbauer for disordered bosons, the Stieltjes-Wigert matrix model of Chern-Simons theory, and Angelesco ensembles.Comment: 20 page

Large Deviations for a Non-Centered Wishart Matrix

We investigate an additive perturbation of a complex Wishart random matrix and prove that a large deviation principle holds for the spectral measures. The rate function is associated to a vector equilibrium problem coming from logarithmic potential theory, which in our case is a quadratic map involving the logarithmic energies, or Voiculescu's entropies, of two measures in the presence of an external field and an upper constraint. The proof is based on a two type particles Coulomb gas representation for the eigenvalue distribution, which gives a new insight on why such variational problems should describe the limiting spectral distribution. This representation is available because of a Nikishin structure satisfied by the weights of the multiple orthogonal polynomials hidden in the background.Comment: 40 page

Canonical moments and random spectral measures

We study some connections between the random moment problem and the random matrix theory. A uniform draw in a space of moments can be lifted into the spectral probability measure of the pair (A,e) where A is a random matrix from a classical ensemble and e is a fixed unit vector. This random measure is a weighted sampling among the eigenvalues of A. We also study the large deviations properties of this random measure when the dimension of the matrix grows. The rate function for these large deviations involves the reversed Kullback information.Comment: 32 pages. Revised version accepted for publication in Journal of Theoretical Probabilit

The biomechanical role of periodontal ligament in bonded and replanted vertically fractured teeth under cyclic biting forces

After teeth are replanted, there are two possible healing responses: periodontal ligament healing or ankylosis with subsequent replacement resorption. The purpose of this study was to compare the fatigue resistance of vertically fractured teeth after bonding the fragments under conditions simulating both healing modes. Thirty-two human premolars were vertically fractured and the fragments were bonded together with Super-Bond C&B. They were then randomly distributed into four groups (BP, CP, CA, BA). The BP and CP groups were used to investigate the periodontal ligament healing mode whilst the BA and CA groups simulated ankylosis. All teeth had root canal treatment performed. Metal crowns were constructed for the CP and CA groups. The BP and BA groups only had composite resin restorations in the access cavities. All specimens were subjected to a 260 N load at 4 Hz until failure of the bond or until 2×106 cycles had been reached if no fracture occurred. Cracks were detected by stereomicroscope imaging and also assessed via dye penetration tests. Finally, interfaces of the resin luting agent were examined by scanning electron microscope. The results confirmed that the fatigue resistance was higher in the groups with simulated periodontal ligament healing. Periodontal reattachment showed important biomechanical role in bonded and replanted vertically fractured teeth