Olla, Stefano 1959
Overview
Works:  10 works in 44 publications in 2 languages and 1,177 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Editor, Thesis advisor, Author 
Classifications:  QC175.2, 530.138 
Publication Timeline
.
Most widely held works by
Stefano Olla
Entropy methods for the Boltzmann equation : lectures from a special semester at the Centre Émile Borel, Institut H. Poincaré,
Paris, 2001 by
Fraydoun Rezakhanlou(
Book
)
17 editions published in 2008 in English and held by 220 WorldCat member libraries worldwide
Entropy and entropy production have recently become mathematical tools for kinetic and hydrodynamic limits, when deriving the macroscopic behaviour of systems from the interaction dynamics of their many microscopic elementary constituents at the atomic or molecular level. During a special semester on Hydrodynamic Limits at the Centre Émile Borel in Paris, 2001 two of the research courses were held by C. Villani and F. Rezakhanlou. Both illustrate the major role of entropy and entropy production in a mutual and complementary manner and have been written up and updated for joint publication. Villani describes the mathematical theory of convergence to equilibrium for the Boltzmann equation and its relation to various problems and fields, including information theory, logarithmic Sobolev inequalities and fluid mechanics. Rezakhanlou discusses four conjectures for the kinetic behaviour of the hard sphere models and formulates four stochastic variations of this model, also reviewing known results for these
17 editions published in 2008 in English and held by 220 WorldCat member libraries worldwide
Entropy and entropy production have recently become mathematical tools for kinetic and hydrodynamic limits, when deriving the macroscopic behaviour of systems from the interaction dynamics of their many microscopic elementary constituents at the atomic or molecular level. During a special semester on Hydrodynamic Limits at the Centre Émile Borel in Paris, 2001 two of the research courses were held by C. Villani and F. Rezakhanlou. Both illustrate the major role of entropy and entropy production in a mutual and complementary manner and have been written up and updated for joint publication. Villani describes the mathematical theory of convergence to equilibrium for the Boltzmann equation and its relation to various problems and fields, including information theory, logarithmic Sobolev inequalities and fluid mechanics. Rezakhanlou discusses four conjectures for the kinetic behaviour of the hard sphere models and formulates four stochastic variations of this model, also reviewing known results for these
Fluctuations in Markov processes : time symmetry and martingale approximation by
Tomasz Komorowski(
Book
)
17 editions published between 2012 and 2014 in English and held by 158 WorldCat member libraries worldwide
Diffusive phenomena in statistical mechanics and in other fields arise from markovian modeling and their study requires sophisticated mathematical tools. In infinite dimensional situations, time symmetry properties can be exploited in order to make martingale approximations, along the lines of the seminal work of Kipnis and Varadhan. The present volume contains the most advanced theories on the martingale approach to central limit theorems. Using the time symmetry properties of the Markov processes, the book develops the techniques that allow us to deal with infinite dimensional models that appear in statistical mechanics and engineering (interacting particle systems, homogenization in random environments, and diffusion in turbulent flows, to mention just a few applications). The first part contains a detailed exposition of the method, and can be used as a text for graduate courses. The second concerns application to exclusion processes, in which the duality methods are fully exploited. The third part is about the homogenization of diffusions in random fields, including passive tracers in turbulent flows (including the superdiffusive behavior). ℗¡ There are no other books in the mathematical literature that deal with this kind of approach to the problem of the central limit theorem. Hence, this volume meets the demand for a monograph on this powerful approach, now widely used in many areas of probability and mathematical physics. The book also covers the connections with and application to hydrodynamic limits and homogenization theory, so besides probability researchers it will also be of interest to mathematical physicists and analysts
17 editions published between 2012 and 2014 in English and held by 158 WorldCat member libraries worldwide
Diffusive phenomena in statistical mechanics and in other fields arise from markovian modeling and their study requires sophisticated mathematical tools. In infinite dimensional situations, time symmetry properties can be exploited in order to make martingale approximations, along the lines of the seminal work of Kipnis and Varadhan. The present volume contains the most advanced theories on the martingale approach to central limit theorems. Using the time symmetry properties of the Markov processes, the book develops the techniques that allow us to deal with infinite dimensional models that appear in statistical mechanics and engineering (interacting particle systems, homogenization in random environments, and diffusion in turbulent flows, to mention just a few applications). The first part contains a detailed exposition of the method, and can be used as a text for graduate courses. The second concerns application to exclusion processes, in which the duality methods are fully exploited. The third part is about the homogenization of diffusions in random fields, including passive tracers in turbulent flows (including the superdiffusive behavior). ℗¡ There are no other books in the mathematical literature that deal with this kind of approach to the problem of the central limit theorem. Hence, this volume meets the demand for a monograph on this powerful approach, now widely used in many areas of probability and mathematical physics. The book also covers the connections with and application to hydrodynamic limits and homogenization theory, so besides probability researchers it will also be of interest to mathematical physicists and analysts
Fluctuations à l'équilibre d'un modèle stochastique non gradient qui conserve l'énergie by
Freddy Hernandez(
Book
)
2 editions published in 2010 in English and held by 2 WorldCat member libraries worldwide
In this thesis we study the equilibrium energy fluctuation field of a onedimensional reversible non gradient model. We prove that the limit fluctuation process is governed by a generalized OrnsteinUhlenbeck process. By adapting the non gradient method introduced by S.R.S Varadhan, we identify the correct diffusion term, which allows us to derive the BoltzmannGibbs principle. This is the key point to show that the energy fluctuation field converges in the sense of finite dimensional distributions to a generalized OrnsteinUhlenbeck process. Moreover, using again the BoltzmannGibbs principle we also prove tightness for the energy fluctuation field in a specified Sobolev space, which together with the finite dimensional convergence implies the convergence in distribution to the generalized OrnsteinUhlenbeck process mentioned above. The fact that the conserved quantity is not a linear functional of the coordinates of the system, introduces new difficulties of geometric nature in applying Varadhan's non gradient method
2 editions published in 2010 in English and held by 2 WorldCat member libraries worldwide
In this thesis we study the equilibrium energy fluctuation field of a onedimensional reversible non gradient model. We prove that the limit fluctuation process is governed by a generalized OrnsteinUhlenbeck process. By adapting the non gradient method introduced by S.R.S Varadhan, we identify the correct diffusion term, which allows us to derive the BoltzmannGibbs principle. This is the key point to show that the energy fluctuation field converges in the sense of finite dimensional distributions to a generalized OrnsteinUhlenbeck process. Moreover, using again the BoltzmannGibbs principle we also prove tightness for the energy fluctuation field in a specified Sobolev space, which together with the finite dimensional convergence implies the convergence in distribution to the generalized OrnsteinUhlenbeck process mentioned above. The fact that the conserved quantity is not a linear functional of the coordinates of the system, introduces new difficulties of geometric nature in applying Varadhan's non gradient method
A microscopic model of heat conduction by
Giada Basile(
Book
)
1 edition published in 2007 in English and held by 1 WorldCat member library worldwide
1 edition published in 2007 in English and held by 1 WorldCat member library worldwide
Homogénéisation de processus de diffusion en milieu aléatoire by
Gaël Benabou(
Book
)
1 edition published in 2005 in French and held by 1 WorldCat member library worldwide
Cette thèse étudie l'homogénéisation du processus d'OrnsteinUhlenbeck dans un milieu aléatoire. Ce processus modélise le mouvement microscopique d'une particule de masse non nulle dans un fluide. On prouvera un théorème central limit pour la trajectoire d'une particule marqée soumise à un potentiel non borné. On montrera également le comportement superdiffusif de la particule dans un champ de vitesses incompressible turbulent et stratifié. Nous ferons des comparaisons avec le cas d'une particule de masse nulle
1 edition published in 2005 in French and held by 1 WorldCat member library worldwide
Cette thèse étudie l'homogénéisation du processus d'OrnsteinUhlenbeck dans un milieu aléatoire. Ce processus modélise le mouvement microscopique d'une particule de masse non nulle dans un fluide. On prouvera un théorème central limit pour la trajectoire d'une particule marqée soumise à un potentiel non borné. On montrera également le comportement superdiffusif de la particule dans un champ de vitesses incompressible turbulent et stratifié. Nous ferons des comparaisons avec le cas d'une particule de masse nulle
Limites hydrodynamiques et fluctuations à l'équilibre pour des systèmes de particules en interaction by
K. L Nagy(
Book
)
1 edition published in 2006 in French and held by 1 WorldCat member library worldwide
This thesis concerns three different models of interacting particle systems. In the first part of the thesis we give an elementary proof of the central limit theorem for one dimensional symmetric random walk in random environment and we derive the hydrodynamic limit of the symmetric simple exclusion in random environment. In the second part we investigate a hyperbolic and nonattractive latticegas model. By means of the method of compensated compactness, logarithmic Sobolev inequalities and the Lax entropy inequality we prove existence and uniqueness of the hydrodynamic limit even in the regime of shocks. In the third part of the thesis we consider a system of harmonic oscillators with multiplicative noise. We show that the equilibrium fluctuations of the conserved fields (energy and deformation) at a diffusive scaling are described by a couple of generalized OrnsteinUhlenbeck processes
1 edition published in 2006 in French and held by 1 WorldCat member library worldwide
This thesis concerns three different models of interacting particle systems. In the first part of the thesis we give an elementary proof of the central limit theorem for one dimensional symmetric random walk in random environment and we derive the hydrodynamic limit of the symmetric simple exclusion in random environment. In the second part we investigate a hyperbolic and nonattractive latticegas model. By means of the method of compensated compactness, logarithmic Sobolev inequalities and the Lax entropy inequality we prove existence and uniqueness of the hydrodynamic limit even in the regime of shocks. In the third part of the thesis we consider a system of harmonic oscillators with multiplicative noise. We show that the equilibrium fluctuations of the conserved fields (energy and deformation) at a diffusive scaling are described by a couple of generalized OrnsteinUhlenbeck processes
Diffusion et fluctuations dans des systèmes conservatifs by
Cédric Bernardin(
Book
)
1 edition published in 2004 in French and held by 1 WorldCat member library worldwide
La thèse se compose de deux parties distinctes et traite de systèmes de particules en interaction. Dans la première partie, nous avons développé les méthodes de dualité généralisée dans trois contextes : régularité d'un coefficient de diffusion, temps d'occupation d'un site dans le processus d'exclusion et fluctuations dans les dynamiques de awasaki. Dans la deuxième partie, nous introduisons un modèle de conduction de la chaleur et étudions le comportement hydrodynamique du système en admettant une conjecture que nous avons pu démontrer dans un cas simple
1 edition published in 2004 in French and held by 1 WorldCat member library worldwide
La thèse se compose de deux parties distinctes et traite de systèmes de particules en interaction. Dans la première partie, nous avons développé les méthodes de dualité généralisée dans trois contextes : régularité d'un coefficient de diffusion, temps d'occupation d'un site dans le processus d'exclusion et fluctuations dans les dynamiques de awasaki. Dans la deuxième partie, nous introduisons un modèle de conduction de la chaleur et étudions le comportement hydrodynamique du système en admettant une conjecture que nous avons pu démontrer dans un cas simple
Milieux aléatoires by
Nina Gantert(
Book
)
1 edition published in 2001 in French and held by 1 WorldCat member library worldwide
1 edition published in 2001 in French and held by 1 WorldCat member library worldwide
Large deviation problems in statistical mechanics by
Stefano Olla(
)
1 edition published in 1987 in English and held by 1 WorldCat member library worldwide
1 edition published in 1987 in English and held by 1 WorldCat member library worldwide
Problèmes de diffusion pour des chaînes d'oscillateurs harmoniques perturbées by
Marielle Simon(
)
1 edition published in 2014 in English and held by 1 WorldCat member library worldwide
The heat equation is known to be a macroscopic phenomenon, emerging after a diffusive rescaling of space and time. In linear systems of interacting oscillators, the energy ballistically disperses and the thermal conductivity is infinite. Since the Fourier law is not valid for linear interactions, nonlinearities in the microscopic dynamics are needed. In order to bring ergodicity to the system, we superpose a stochastic energy conserving perturbation to the underlying deterministic dynamics.In the first part we study the Hamiltonian dynamics of linear coupled oscillators, which are perturbed by a degenerate conservative stochastic noise. The latter flips the sign of the velocities at random times. The evolution yields two conservation laws (the energy and the length of the chain), and the macroscopic behavior is given by a nonlinear parabolic system.Then, we suppose the harmonic oscillators to evolve in a random environment, in addition to be stochastically perturbed. The noise is very degenerate, and we prove a macroscopic behavior that holds at equilibrium: precisely, energy fluctuations at equilibrium evolve according to an infinite dimensional OrnsteinUhlenbeck process driven by the linearized heat equation.Finally, anomalous behaviors have been observed for onedimensional systems which preserve momentum in addition to the energy. In the third part, we consider two different perturbations, the first one preserving the momentum, and the second one destroying that new conservation law. When the intensity of the second noise is decreasing, we observe (in a suitable time scale) a phase transition between a regime of normal diffusion and a regime of superdiffusion
1 edition published in 2014 in English and held by 1 WorldCat member library worldwide
The heat equation is known to be a macroscopic phenomenon, emerging after a diffusive rescaling of space and time. In linear systems of interacting oscillators, the energy ballistically disperses and the thermal conductivity is infinite. Since the Fourier law is not valid for linear interactions, nonlinearities in the microscopic dynamics are needed. In order to bring ergodicity to the system, we superpose a stochastic energy conserving perturbation to the underlying deterministic dynamics.In the first part we study the Hamiltonian dynamics of linear coupled oscillators, which are perturbed by a degenerate conservative stochastic noise. The latter flips the sign of the velocities at random times. The evolution yields two conservation laws (the energy and the length of the chain), and the macroscopic behavior is given by a nonlinear parabolic system.Then, we suppose the harmonic oscillators to evolve in a random environment, in addition to be stochastically perturbed. The noise is very degenerate, and we prove a macroscopic behavior that holds at equilibrium: precisely, energy fluctuations at equilibrium evolve according to an infinite dimensional OrnsteinUhlenbeck process driven by the linearized heat equation.Finally, anomalous behaviors have been observed for onedimensional systems which preserve momentum in addition to the energy. In the third part, we consider two different perturbations, the first one preserving the momentum, and the second one destroying that new conservation law. When the intensity of the second noise is decreasing, we observe (in a suitable time scale) a phase transition between a regime of normal diffusion and a regime of superdiffusion
Audience Level
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Related Identities
 Rezakhanlou, Fraydoun Author
 Golse, François Editor
 Villani, Cédric 1973
 Landim, Claudio 1965 Opponent Thesis advisor
 Komorowski, Tomasz 1963 Author
 Centre Émile Borel
 Université ParisDauphine Degree grantor
 Bernardin, Cédric (1977....). Opponent Thesis advisor Author
 Hernandez, Freddy (1978 ...). Author
 Basile, Giada (1979 ...). Author
Associated Subjects
Central limit theorem Differential equations, Partial Distribution (Probability theory) Entropy Fluctuations (Physics) Hydrodynamics Large deviations Markov processes Markov processesMathematical models Martingales (Mathematics) Mathematical physics Mathematics MaxwellBoltzmann distribution law Statistical mechanics Stochastic processes Transport theory