1,720,966 research outputs found
The Impact of Disorder in the Critical Dynamics of Mean-Field Models
Full text linkWe consider a mean-field interacting particle system embedded in a site-dependent and i.i.d. random environment. We make it evolve as a continuous time Markov chain on its state space. The dynamics are given depending on few parameters and they are completely described by that of the order parameter of the model. We derive the dynamics of this last quantity, in the infinite volume limit, and then their long time behavior is studied. The limiting dynamics of the order parameter are deterministic and, depending on the values of the parameters, exhibit a phase transition. Our main interest is the study of the critical fluctuations, that are the fluctuations of the order parameter around its limiting dynamics when the parameters take the values for which the phase transition occurs. We aim at analyzing the effect of the disorder in the dynamics of them, as compared with the homogeneous case. We deal with spin-flip and interacting diffusion systems, but we do not treat the subject in total generality, we focus on specific models: the random Curie-Weiss model; a non-reversible spin-flip system motivated by Finance and the homogeneous and inhomogeneous Kuramoto models.Consideriamo un sistema di particelle interagenti a campo-medio immerso in un ambiente aleatorio i.i.d. e sito-dipendente. Il sistema viene fatto evolvere come una catena di Markov a tempo continuo sullo spazio degli stati. La dinamica dipende da pochi parametri e puo` essere completamente descritta attraverso quella del parametro d'ordine del modello. Ricaviamo la dinamica di quest'ultimo nel limite di volume infinito e quindi ne studiamo il comportamento per tempi lunghi. Tale dinamica limite risulta essere deterministica e, al variare dei parametri, presenta una transizione di fase. Il nostro interesse principale e` lo studio delle fluttuazioni critiche, cioe` le fluttuazioni del parametro d'ordine attorno alla dinamica limite quando i parametri assumono i valori tali per cui si verifica la transizione di fase. Lo scopo e` l'analisi degli effetti causati dal disordine su di esse, confrontandole con le analoghe fluttuazioni per il caso omogeneo. Trattiamo sistemi di spin e di diffusioni, ma non in totale generalita`. Ci concentriamo su dei modelli specifici: il modello di Curie-Weiss con aggiunta di campo aleatorio; un sistema di spin non-reversibile motivato dalla Finanza e il modello di Kuramoto omogeneo e non
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
Collective periodicity in mean-field models of cooperative behavior
No full textWe 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 ferromag- netic type, then its dissipative counterpart exhibits periodic orbits in the thermodynamic limit
Merging exchangeable occupancy models: M(a)-models and their relation to the maximum entropy principle
No full textIn this paper a new transformation of occupancy models, called merging, is introduced. In particular, it will be studied the effect of merging on a class of occupancy models that was recently introduced in Collet, Leisen, Spizzichino and Suter (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
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
The role of disorder in the dynamics of critical fluctuations of mean field models
Full text linkThe purpose of this paper is to analyze how 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 concerns 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)
Strong existence and uniqueness of the stationary distribution for a stochastic inviscid dyadic model
Full text linkWe consider an inviscid stochastically forced dyadic model, where the additive noise acts only on the first component. We prove that a strong solution for this problem exists and is unique by means of uniform energy estimates. Moreover, we exploit these results to establish strong existence and uniqueness of the stationary distribution
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
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