Macroscopic limit of a bipartite Curie-Weiss model: a dynamical approach

We analyze the Glauber dynamics for a bi-populated Curie-Weiss model. We obtain the limiting behavior of the empirical averages in the limit of infinitely many particles. We then characterize the phase space of the model in absence of magnetic field and we show that several phase transitions in the inter-groups interaction strength occur.Comment: 18 pages, 3 figure

The role of disorder in the dynamics of critical fluctuations of mean field models

The purpose of this paper is to analyze how the disorder affects the dynamics of critical fluctuations for two different types of interacting particle system: the Curie-Weiss and Kuramoto model. The models under consideration are a collection of spins and rotators respectively. They both are subject to a mean field interaction and embedded in a site-dependent, i.i.d. random environment. As the number of particles goes to infinity their limiting dynamics become deterministic and exhibit phase transition. The main result concern the fluctuations around this deterministic limit at the critical point in the thermodynamic limit. From a qualitative point of view, it indicates that when disorder is added spin and rotator systems belong to two different classes of universality, which is not the case for the homogeneous models (i.e., without disorder).Comment: 41 page

Collective periodicity in mean-field models of cooperative behavior

We propose a way to break symmetry in stochastic dynamics by introducing a dissipation term. We show in a specific mean-field model, that if the reversible model undergoes a phase transition of ferromagnetic type, then its dissipative counterpart exhibits periodic orbits in the thermodynamic limit.Comment: 19 pages, 3 figure

Free completely random measures

Free probability is a noncommutative probability theory introduced by Voiculescu where the concept of independence of classical probability is replaced by the concept of freeness. An important connection between free and classical infinite divisibility was established by Bercovici and Pata (1999) in form of a bijection, mapping the class of classical infinitely divisible laws into the class of free infinitely divisible laws. A particular class of infinitely divisible laws are the completely random measures introduced by Kingman (1967). In this paper, a free analogous of completely random measures is introduced and, a free Poisson process characterization is provided as well as a representation through a free cumulant transform. Furthermore, some examples are displayed.Bayesian non parametrics, Bercovici-Pata bijection, Free completely random measures, Free infinite divisibility, Free probability

Free completely random measures

Free probability is a noncommutative probability theory introduced by Voiculescu where the concept of independence of classical probability is replaced by the concept of freeness. An important connection between free and classical infinite divisibility was established by Bercovici and Pata (1999) in form of a bijection, mapping the class of classical infinitely divisible laws into the class of free infinitely divisible laws. A particular class of infinitely divisible laws are the completely random measures introduced by Kingman (1967). In this paper, a free analogous of completely random measures is introduced and, a free Poisson process characterization is provided as well as a representation through a free cumulant transform. Furthermore, some examples are displayed

The chemical composition of red giants in 47 Tucanae I: Fundamental parameters and chemical abundance patterns

Context: The study of chemical abundance patterns in globular clusters is of key importance to constrain the different candidates for intra-cluster pollution of light elements. Aims: We aim at deriving accurate abundances for a large range of elements in the globular cluster 47 Tucanae (NGC 104) to add new constraints to the pollution scenarios for this particular cluster, expanding the range of previously derived element abundances. Methods: Using tailored 1D LTE atmospheric models together with a combination of equivalent width measurements, LTE, and NLTE synthesis we derive stellar parameters and element abundances from high-resolution, high signal-to-noise spectra of 13 red giant stars near the tip of the RGB. Results: We derive abundances of a total 27 elements (O, Na, Mg, Al, Si, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Y, Zr, Mo, Ru, Ba, La, Ce, Pr, Nd, Eu, Dy). Departures from LTE were taken into account for Na, Al and Ba. We find a mean [Fe/H] = $-0.78\pm0.07$ and $[\alpha/{\rm Fe}]=0.34\pm0.03$ in good agreement with previous studies. The remaining elements show good agreement with the literature, but the inclusion of NLTE for Al has a significant impact on the behaviour of this key element. Conclusions: We confirm the presence of an Na-O anti-correlation in 47 Tucanae found by several other works. Our NLTE analysis of Al shifts the [Al/Fe] to lower values, indicating that this may be overestimated in earlier works. No evidence for an intrinsic variation is found in any of the remaining elements.Comment: 22 pages, 16 figures. Accepted for publication in A&