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Academic literature on the topic 'Grandes déviations dynamiques'
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Dissertations / Theses on the topic "Grandes déviations dynamiques"
Tailleur, Julien. "Grandes déviations, physique statistique et systèmes dynamiques." Phd thesis, Université Pierre et Marie Curie - Paris VI, 2007. http://tel.archives-ouvertes.fr/tel-00325956.
Full textNguyen, Thu Lam Khanh-Dang. "Problèmes de grandes déviations dans les systèmes dynamiques." Paris 6, 2013. http://www.theses.fr/2013PA066146.
Full textIn this thesis we are interested in large deviations in dynamical systems. We use ideas and methods both from the statistical physics field and the dynamical systems field. In a first part, we test the idea that large deviations in chaotic dynamical systems are typically associated to ordered trajectories. We first minimize a simple functionnal of the trajectories of the baker's map. Although most of the trajectories are aperiodic, we find that minimal trajectories are periodic. In a second model, we study a density free energy functionnal with a glassy phenomenology: first order transition between a liquid and a crystal and appereance of a huge number of metastable and amorphous states. The state of minimum free energy is nevers amorphous. In a second part, we consider two problems that arises when using the so-called Lyapunov Weigted Dynamics, used numerically to sample large deviations of chaoticity in a dynamical system. (i) We analyse hamiltonian dynamics perturbed stochastically and show that the presence of noise destabilize the system, unless the initial condition is taken in a isochronous part of the phase space. (ii) We study the dynamics of a population of two species in dynamical equilibrium when a selection process comes into play. The finite size of the population allows for the extinction of one of the species
Rabeherimanana, Toussaint Joseph. "Petites perturbations de systèmes dynamiques et algèbre de Lie nilpotentes." Paris 7, 1992. http://www.theses.fr/1992PA077163.
Full textPrieur, Clémentine. "Dépendance faible: estimation et théorèmes limite.Application à l'étude statistique de certains systèmes dynamiques." Habilitation à diriger des recherches, Université Paul Sabatier - Toulouse III, 2006. http://tel.archives-ouvertes.fr/tel-00133468.
Full textnon -mélangeantes au sens de Rosenblatt (1956). La notion de mélange classique est affaiblie
afin d'établir des inégalités ainsi que des théorèmes limite pour différentes classes de processus
comme par exemple certains systèmes dynamiques, des chaînes de Markov non irréductibles,
ou encore des fonctions de processus linéaires non mélangeants. Les résultats obtenus sont
ensuite appliqués au domaine de la statistique non paramétrique.
Deux autres thématiques sont abordées dans ce manuscrit : d'une part l'étude de principes
de grandes déviations (notamment pour le processus de records généralisés), et d'autre part
l'estimation adaptative de fonctionnelles linéaires.
Barret, Florent. "Temps de transitions métastables pour des systèmes dynamiques stochastiques fini et infini-dimensionnels." Phd thesis, Palaiseau, Ecole polytechnique, 2012. https://theses.hal.science/docs/00/71/57/87/PDF/these.pdf.
Full textIn this thesis, we work on metastability for some stochastic dynamical systems. More precisely, we study some differential or partial differential equations perturbed by an additive white noise in the small noise asymptotic. We compute the expectation of the transition times for some models (so-called Eyring-Kramers Formula). First we generalize some known results for Itô diffusions whose drift is given by the gradient of a potential. We give an equivalence between the geometry of the potential and an electrical network which allows a simple computation of the transition times between minima of the potential. To do so, we use potential theory and capacities. The main result of this thesis is about a class of scalar, parabolic, semi-linear stochastic partial differential equations perturbed by a space-time white noise on a bounded real interval as the Allen-Cahn model. These equations are similar to the gradient drift diffusions but in infinite dimension. We consider Dirichlet or Neumann boundary conditions and discuss the periodic boundary conditions. Under some assumptions, we prove a formula, similar to the finite dimensional case, for the transition times. In the proof, we use a finite difference approximation and a coupling and apply the finite dimensional estimates to the approximation. We prove the uniformity of the estimates in the dimension and then we take the limit to recover the infinite dimensional equation
Barret, Florent. "Temps de transitions métastables pour des systèmes dynamiques stochastiques fini et infini-dimensionnels." Phd thesis, Ecole Polytechnique X, 2012. http://tel.archives-ouvertes.fr/tel-00715787.
Full textBouley, Angèle. "Grandes déviatiοns statistiques de l'exclusiοn en cοntact faible avec des réservοirs." Electronic Thesis or Diss., Normandie, 2024. http://www.theses.fr/2024NORMR032.
Full textThis thesis focuses on a process of exclusion in weak contact with reservoirs. More precisely, we revisit the model studied in the article "Hydrostatics and dynamical large deviations of boundary driven gradient symmetric exclusion processes" by J. Farfan, C. Landim, M. Mourragui but in the case of weak (rather than strong) contact with the reservoirs. Through this weak contact, results are modified such as the hydrodynamic limit theorem and the theorem of large dynamical deviations. The modifications of these two results are studied in this thesis in the case of dimension 1. The first part of the thesis will consist of proving the hydrodynamic limit theorem for our model, i.e. showing the convergence of the empirical measure. Based on the steps in Section 5 of the book "Scaling limits of interacting particle systems" by C. Kipnis, C. Landim, we will show that this sequence is relatively compact before studying the properties of its limit points. For each convergent subsequence, we will show that they converge to limit points that concentrate on absolutely continuous trajectories and whose densities are weak solutions of an equation that we will call the hydrodynamic equation. By demonstrating the uniqueness of weak solutions of the hydrodynamic equation, we will then have a unique limit point and the convergence of the sequence will be established. In the second part of the thesis, we will demonstrate the theorem of large dynamical deviations, i.e. that there exists a rate function I_{[0,T]}(.|\gamma) satisfying the large deviations principle for the sequence studied in the first part. After defining the rate function, we will show that it is lower semicontinuous, has compact level sets, and satisfies a lower bound and an upper bound property. One of the main challenges will be to show a density property for a set F. This will represent a significant part of this section. Moreover, to prove this density property, we will need to decompose the function I_{[0,T]}(.|\gamma) which contains boundary terms and does not have a convexity property like the rate functions of several existing models. Due to these two constraints, new regularity properties as well as a new type of decomposition will be demonstrated
Rivière, Gabriel. "Délocalisation des mesures semi-classiques pour des systèmes dynamiques chaotiques." Palaiseau, Ecole polytechnique, 2009. http://pastel.paristech.org/5721/01/these-riviere-final.pdf.
Full textTran, Viet Chi. "Modèles particulaires stochastiques pour des problèmes d'évolution adaptative et pour l'approximation de solutions statistiques." Phd thesis, Université de Nanterre - Paris X, 2006. http://tel.archives-ouvertes.fr/tel-00125100.
Full textChampagnat, Nicolas. "Étude mathématique de modèles stochastiques d'évolution issus de la théorie écologique des dynamiques adaptatives." Phd thesis, Université de Nanterre - Paris X, 2004. http://tel.archives-ouvertes.fr/tel-00091929.
Full textConference papers on the topic "Grandes déviations dynamiques"
Baranes, M., and T. Fortin. "Planification et chirurgie guidée - Avis d’experts : Apports des nouvelles technologies en implantologie : de la planification à la réalisation de la prothèse provisoire immédiate." In 66ème Congrès de la SFCO. Les Ulis, France: EDP Sciences, 2020. http://dx.doi.org/10.1051/sfco/20206601011.
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