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Documents  35Q82 | enregistrements trouvés : 6

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The aim of this series of lectures is to explain what the weak KPZ universality conjecture is, and to present a proof of it in the stationary case.
Lecture 1: The KPZ equation, the KPZ universality class and the weak and strong KPZ universality conjectures.
Lecture 2: The martingale approach and energy solutions of the KPZ equation.
Lecture 3: A proof of the weak KPZ universality conjecture in the stationary case.

35Q82 ; 60K35 ; 82C22 ; 82C24

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The aim of this series of lectures is to explain what the weak KPZ universality conjecture is, and to present a proof of it in the stationary case.
Lecture 1: The KPZ equation, the KPZ universality class and the weak and strong KPZ universality conjectures.
Lecture 2: The martingale approach and energy solutions of the KPZ equation.
Lecture 3: A proof of the weak KPZ universality conjecture in the stationary case.

35Q82 ; 60K35 ; 82C22 ; 82C24

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The aim of this series of lectures is to explain what the weak KPZ universality conjecture is, and to present a proof of it in the stationary case.
Lecture 1: The KPZ equation, the KPZ universality class and the weak and strong KPZ universality conjectures.
Lecture 2: The martingale approach and energy solutions of the KPZ equation.
Lecture 3: A proof of the weak KPZ universality conjecture in the stationary case.

35Q82 ; 60K35 ; 82C22 ; 82C24

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We propose a mean field kinetic model for systems of rational agents interacting in a game theoretical framework. This model is inspired from non-cooperative anonymous games with a continuum of players and Mean-Field Games. The large time behavior of the system is given by a macroscopic closure with a Nash equilibrium serving as the local thermodynamic equilibrium. Applications of the presented theory to social and economical models will be given.
We propose a mean field kinetic model for systems of rational agents interacting in a game theoretical framework. This model is inspired from non-cooperative anonymous games with a continuum of players and Mean-Field Games. The large time behavior of the system is given by a macroscopic closure with a Nash equilibrium serving as the local thermodynamic equilibrium. Applications of the presented theory to social and economical models will be ...

91B80 ; 35Q82 ; 35Q91

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We are concerned with deriving sharp exponential decay estimates (i.e. with maximum rate and minimum multiplicative constant) for linear, hypocoercive evolution equations. Using a modal decomposition of the model allows to assemble a Lyapunov functional using Lyapunov matrix inequalities for each Fourier mode.
We shall illustrate the approach on the 1D Goldstein-Taylor model, a2-velocity transport-relaxation equation. On the torus the lowest Fourier modes determine the spectral gap of the whole equation in $L^{2}$. By contrast, on the whole real line the Goldstein-Taylor model does not have a spectral gap, since the decay rate of the Fourier modes approaches zero in the small mode limit. Hence, the decay is reduced to algebraic.
In the final part of the talk we consider the Goldstein-Taylor model with non-constant relaxation rate, which is hence not amenable to a modal decomposition. In this case we construct a Lyapunov functional of pseudodifferential nature, one that is motivated by the modal analysis in the constant case.The robustness of this approach is illustrated on a multi-velocity GoldsteinTaylor model, yielding explicit rates of convergence to the equilibrium.
This is joint work with J. Dolbeault, A. Einav, C. Schmeiser, B. Signorello, and T. Wöhrer.
We are concerned with deriving sharp exponential decay estimates (i.e. with maximum rate and minimum multiplicative constant) for linear, hypocoercive evolution equations. Using a modal decomposition of the model allows to assemble a Lyapunov functional using Lyapunov matrix inequalities for each Fourier mode.
We shall illustrate the approach on the 1D Goldstein-Taylor model, a2-velocity transport-relaxation equation. On the torus the lowest ...

82C40 ; 35B40 ; 35Q82 ; 35S05

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