1,721,018 research outputs found
Synchronization and Spin-Flop Transitions for a Mean-Field XY Model in Random Field
Full text linkWe characterize the phase space for the infinite volume limit of a ferromagnetic mean-field XY model in a random field pointing in one direction with two symmetric values. We determine the stationary solutions and detect possible phase transitions in the interaction strength for fixed random field intensity. We show that at low temperature magnetic ordering appears perpendicularly to the field. The latter situation corresponds to a spin-flop transition
Path-space moderate deviations for a class of Curie–Weiss models with dissipation
Full text linkWe modify the spin-flip dynamics of the Curie–Weiss model with dissipation in Dai Pra, Fischer and Regoli (2013) by considering arbitrary transition rates and we analyze the phase-portrait as well as the dynamics of moderate fluctuations for macroscopic observables. We obtain path-space moderate deviation principles via a general analytic approach based on the convergence of non-linear generators and uniqueness of viscosity solutions for associated Hamilton–Jacobi equations. The moderate asymptotics depend crucially on the phase we are considering and, moreover, their behavior may be influenced by the choice of the rates
Macroscopic Limit of a Bipartite Curie–Weiss Model: A Dynamical Approach
No full textWe 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
Effects of Local Fields in a Dissipative Curie-Weiss Model: Bautin Bifurcation and Large Self-sustained Oscillations
No full textWe modify the spin-flip dynamics of a Curie-Weiss model with dissipative interaction potential (Dai Pra, Fischer and Regoli (2013)) by adding a site-dependent i.i.d. random magnetic field. The purpose is to analyze how the addition of the field affects the time-evolution of the observables in the macroscopic limit. Our main result shows that a Bautin bifurcation point exists and that, whenever the field intensity is sufficiently strong and the temperature sufficiently low, a periodic orbit emerges through a global bifurcation in the phase space, giving origin to a large-amplitude rhythmic behavior
Dynamical moderate deviations for the Curie-Weiss model
No full textWe derive moderate deviation principles for the trajectory of the empirical magnetization of the standard Curie–Weiss model via a general analytic approach based on convergence of generators and uniqueness of viscosity solutions for associated Hamilton–Jacobi equations. The moderate asymptotics depend crucially on the phase under consideration.Applied Probabilit
Path-space moderate deviation principles for the random field curie-weiss model
Full text linkWe analyze the dynamics of moderate fluctuations for macroscopic observables of the random field Curie-Weiss model (i.e., standard Curie-Weiss model embedded in a site-dependent, i.i.d. random environment). We obtain path-space moderate deviation principles via a general analytic approach based on convergence of nonlinear generators and uniqueness of viscosity solutions for associated Hamilton-Jacobi equations. The moderate asymptotics depend crucially on the phase we consider and moreover, the space-time scale range for which fluctuations can be proven is restricted by the addition of the disorder.</p
Merging Exchangeable Occupancy Distributions: The Family M^(a) and its Connection with the Maximum Entropy Principle
No full textIn this paper a new transformation of occupancy distributions, called merging, is introduced. In particular, it will be studied the effect of merging on a class of occupancy distributions that was recently introduced in Collet et al. (Probab Eng Inf Sci. 27:533-552 2013). These results have an interesting interpretation in the so-called entropy maximization inference. The last part of the paper is devoted to highlight the impact of our findings in this research area
Path-space moderate deviations for a Curie-Weiss model of self-organized criticality
Full text linkThe dynamical Curie-Weiss model of self-organized criticality (SOC) was introduced in (Ann. Inst. Henri Poincaré Probab. Stat. 53 (2017) 658-678) and it is derived from the classical generalized Curie-Weiss by imposing a microscopic Markovian evolution having the distribution of the Curie-Weiss model of SOC (Ann. Probab. 44 (2016) 444-478) as unique invariant measure. In the case of Gaussian single-spin distribution, we analyze the dynamics of moderate fluctuations for the magnetization. We obtain a path-space moderate deviation principle via a general analytic approach based on convergence of non-linear generators and uniqueness of viscosity solutions for associated Hamilton-Jacobi equations. Our result shows that, under a peculiar moderate space-time scaling and without tuning external parameters, the typical behavior of the magnetization is critical
Completely random measures and Lévy bases in free probability
Full text linkThis paper develops a theory for completely random measures in the framework of free probability. A general existence result for free completely random measures is established, and in analogy to the classical work of Kingman it is proved that such random measures can be decomposed into the sum of a purely atomic part and a (freely) infinitely divisible part. The latter part (termed a free Lévy basis) is studied in detail in terms of the free Lévy-Khintchine representation and a theory parallel to the classical work of Rajput and Rosiński is developed. Finally a Lévy-Itô type decomposition for general free Lévy bases is established
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