Dissertations / Theses on the topic 'Grandes déviations dynamiques'
Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles
Consult the top 19 dissertations / theses for your research on the topic 'Grandes déviations dynamiques.'
Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.
You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.
Browse dissertations / theses on a wide variety of disciplines and organise your bibliography correctly.
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 textTangarife, Tomás. "Théorie cinétique et grandes déviations en dynamique des fluides géophysiques." Thesis, Lyon, École normale supérieure, 2015. http://www.theses.fr/2015ENSL1037/document.
Full textThis thesis deals with the dynamics of geophysical turbulent flows at large scales, more particularly their organization into east-west parallel flows (zonal jets). These structures have the particularity to evolve much slower than the surrounding turbulence. Besides, over long time scales, abrupt transitions between different configurations of zonal jets are observed in some cases (multistability). Our approach consists in averaging the effect of fast turbulent degrees of freedom in order to obtain an effective description of the large scales of the flow, using stochastic averaging and the theory of large deviations. These tools provide theattractors, the typical fluctuations and the large fluctuations of jet dynamics. This allows to go beyond previous studies, which only describe the average jet dynamics. Our first result is an effective equation for the slow dynamics of jets, the validityof this equation is studied from a theoretical point of view, and the physical consequences are discussed. In order to describe the statistics of rare events such as abrupt transitions between different jet configurations, tools from large deviation theory are employed. Original methods are developped in order to implement this theory, those methods can be applied for instance in situations of multistability
Laffargue, Tanguy. "Grandes déviations d'exposants de Lyapunov dans les systèmes étendus." Sorbonne Paris Cité, 2015. http://www.theses.fr/2015USPCC084.
Full textLyapunov exponents are natural observables to quantify the chaoticity of a trajectory. They thus appear as good candidates to discriminate between different dynamical regimes, allowing to study phenomena such as the onset of turbulence which goes hand in hand with the emergence of chaotic trajectories in an otherwise regular flow—or the glass transition—which can be seen as a transition from diffusive dynamics to an arrested, frozen-in, and ergodicity-breaking regime. The present thesis strives to apply the thermodynamic formalism of Sinai, Ruelle and Bowen which transposes in trajectory space the language of equilibrium statistical physics—to fluctuations of Lyapunov exponents in spatially extended systems, for which only few results are available. We begin by presenting a numerical method to sample trajectories of atypical chaoticity in spatially extended systems, hence revealing their various dynamical structures. We also exhibit how this algorithm can be used to measure the dynamical free energy, opening the way for the study of dynamical phase transitions resulting from the possible coexistence of these structures. This method is in particular applied to the Fermi-Pasta-Ulam-Tsingou (FPU) chain of anharmonic oscillators. Next, we show how fluctuations of the largest Lyapunov exponent in systems of interacting particles with underlying diffusive dynamics can be analytically characterized. Carrying out this program allows us to establish interesting connections with damage spreading and reaction-diffusion processes
Laredo, Catherine. "Dynamique de populations dans l'asymptotique des grandes déviations : statistiques de diffusions partiellement observées." Paris 11, 1987. http://www.theses.fr/1987PA112060.
Full textThe first part of this thesis is devoted to the study of spatial branching processes using large deviations techniques. We first obtain a spatial generalization of the Malthusian parameter. Then, we prove the almost everywhere continuity of a monotone operator describing the asymptotic behavior of a nonhomogeneous spatial branching process. Finally, for populations with controlled offspring, we compare a deterministic modelisation (reaction-diffusion) and a stochastic modelisation (controlled branching processes) using numerical methods. The second part is concerned with the non-parametric and parametric inference for the drift function of a diffusion processe (Xt) on R, when one only observes either the first hitting times process (Ta) of increasing levels a, or the flat stretches of Xt, = sup (Xs, st) with length greater than η > 0, between two precribed levels x = Xo and A > x. For diffusions having positive drift, we prove that these observations are asymptotically sufficient with respect to the complete observation of (Xt) up to TA, when the variance of (Xt) and η, for the second observation, go simultaneously to O. We constuct estimators based on these observations. They are shown to be asymptotically normal, asymptotically equivalent to the maximum likelihood estimator based on the observation of (Xt) up to TA. We study in the third part models for cereal domestication
Berglund, Nils. "Equations différentielles stochastiques singulièrement perturbées." Habilitation à diriger des recherches, Université du Sud Toulon Var, 2004. http://tel.archives-ouvertes.fr/tel-00004304.
Full textRouault, Alain. "Quelques études sur les processus de branchement : dynamique de populations dans l'asymptotique des grandes déviations." Paris 11, 1985. http://www.theses.fr/1985PA112260.
Full textFirst we present two studies in branching processes, one about Zipf’s laws, another one about joint estimation of Galton-Watson parameters. Then for spatial branching models, we prove in the large deviation scaling, deterministic limit results for logarithms of populations (generalization of Malthusian parameter, construction of typical genealogies). In the general markovian case, log-populations and log-expectations have not the same limit and an original optimization problem takes place
Chazottes, Jean-René (19. "Entropie relative, dynamique symbolique et turbulence/ Jean-René Chazottes." Aix-Marseille 1, 1999. http://www.theses.fr/1999AIX11028.
Full textBarré, Julien. "Mécanique statistique et dynamique hors équilibre de systèmes avec interactions à longue portée." Lyon, École normale supérieure (sciences), 2003. http://www.theses.fr/2003ENSL0253.
Full textIn the presence of long range interactions, physics is very peculiar : energy is no more additive, phase separation in the usual sense is impossible, dynamics is necessarily coherent on a global scale. . . These peculiarities are independent of the origin of the long range interaction involved, which may be of many different types : gravitational, interaction between vortices in 2D turbulence, unshielded Coulombic interaction, wave-particles couplings for instance. The goal of this thesis is to explore precisely the universality of behaviours in these long range interaction systems; we start from the analysis of toy models, aiming at general results and methods. In a first part, we study equilibrium statistical mechanics which, as is known, may be anomalous and show for instance negative specific heat, or inequivalence between statistical ensembles. We show these anomalies around a tricritical point on an exactly solvable mean field spin model. We then use a general method, based on large deviation theory, to solve the statistical mechanics of long range interaction systems, and we apply it to a number of examples, whose microcanonical solution was till now inaccessible. From these results, and using singularity theory, we are able to classify all the possible inequivalence of ensembles situations. In a second part, we study the out of equilibrium dynamics of long range interacting systems : we explain in details an example of structure formation, and then we present and illustrate a general scenario for slow relaxation to equilibrium, based on the tight link with Vlasov equation. Finally, we apply the previous ideas and methods to a model of free electron laser on a linear accelerator, which yields an original approach, complementary to the usual purely dynamical one for this type of lasers
Feliachi, Ouassim. "From Particles to Fluids : A Large Deviation Theory Approach to Kinetic and Hydrodynamical Limits." Electronic Thesis or Diss., Orléans, 2023. http://www.theses.fr/2023ORLE1063.
Full textThe central problem of statistical physics is to understand how to describe a system with macroscopic equations, which are usually deterministic, starting from a microscopic description, which may be stochastic. This task requires taking at least two limits: a “large N ” limit and a “local equilibrium” limit. The former allows a system of N particles to be described by a phase-space distribution function, while the latter reflects the separation of time scales between the fast approach to local equilibrium and the slow evolution of hydrodynamic modes. When these two limits are taken, a deterministic macroscopic description is obtained. For both theoretical and modeling reasons (N is large but not infinite, the time-scale separation is not perfect), it is sometimes important to understand the fluctuations around this macroscopic description. Fluctuating hydrodynamics provides a framework for describing the evolution of macroscopic, coarse-grained fields while taking into account finite- particle-number induced fluctuations in the hydrodynamic limit. This thesis discusses the derivation of fluctuating hydrodynamics from the microscopic description of particle dynamics. The derivation of the fluctuating hydrodynamics is twofold. First, the “large N” limit must be refined to account for fluctuations beyond the average behavior of the system. This is done by using large deviation theory to establish kinetic large deviation principles that describe the probability of any evolution path for the empirical measure beyond the most probable path described by the kinetic equation. Then, the fluctuating hydrodynamics is derived by studying the hydrodynamical limit of the kinetic large deviation principle, or the associated fluctuating kinetic equation. This dissertation discusses this program and its application to several physical systems ranging from the dilute gas to active particles
Gradinaru, Mihai. "Applications du calcul stochastique à l'étude de certains processus." Habilitation à diriger des recherches, Université Henri Poincaré - Nancy I, 2005. http://tel.archives-ouvertes.fr/tel-00011826.
Full textentre 1996 et 2005, après la thèse de doctorat de l'auteur, et concerne l'étude fine de
certains processus stochastiques : mouvement brownien linéaire ou plan, processus de diffusion,
mouvement brownien fractionnaire, solutions d'équations différentielles stochastiques ou
d'équations aux dérivées partielles stochastiques.
La thèse d'habilitation s'articule en six chapitres correspondant aux thèmes
suivants : étude des intégrales par rapport aux temps locaux de certaines diffusions,
grandes déviations pour un processus obtenu par perturbation brownienne d'un système
dynamique dépourvu de la propriété d'unicité des solutions, calcul stochastique
pour le processus gaussien non-markovien non-semimartingale mouvement brownien fractionnaire,
étude des formules de type Itô et Tanaka pour l'équation de la chaleur stochastique,
étude de la durée de vie du mouvement brownien plan réfléchi dans un domaine à
frontière absorbante et enfin, estimation non-paramétrique et construction d'un
test d'adéquation à partir d'observations discrètes pour le coefficient de diffusion d'une
équation différentielle stochastique.
Les approches de tous ces thèmes sont probabilistes et basées sur l'analyse stochastique.
On utilise aussi des outils d'équations différentielles, d'équations aux dérivées partielles
et de l'analyse.