Manh Hong Duong

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In this paper we discuss the connections between a Vlasov-Fokker-Planck equation and an underlying microscopic particle system, and we interpret those connections in the context of the GENERIC framework (¨ Ottinger 2005). This interpretation provides (a) a variational formulation for GENERIC systems, (b) insight into the origin of this variational(More)
We study the Fokker-Planck equation as the thermodynamic limit of a stochastic particle system on one hand and as a Wasserstein gradient flow on the other. We write the rate functional, which characterizes the large deviations from the thermodynamic limit, in such a way that the free energy appears explicitly. Next we use this formulation via the(More)
In this paper, we analyze the mean number E(n, d) of internal equilibria in a general d-player n-strategy evolutionary game where the agents' payoffs are normally distributed. First, we give a computationally implementable formula for the general case. Next we characterize the asymptotic behavior of E(2, d), estimating its lower and upper bounds as d(More)
In this paper we present a variational technique that handles coarse-graining and passing to a limit in a unified manner. The technique is based on a duality structure, which is present in many gradient flows and other variational evolutions, and which often arises from a large-deviations principle. It has three main features: (A) a natural interaction(More)
In 1998, Jordan-Kinderleher-Otto [JKO98] proved a remarkable result that the diffusion equation can be seen as a gradient flow of the Boltzmann entropy with respect to the Wasserstein distance. This result has sparked off a large body of research in the field of partial differential equations and others in the last two decades. Many evolution equations have(More)
In this paper, we study the distribution and behaviour of internal equilibria in a d-player n-strategy random evolutionary game where the game payoff matrix is generated from normal distributions. The study of this paper reveals and exploits interesting connections between evolutionary game theory and random polynomial theory. The main contributions of the(More)
In this paper, we study the Wasserstein gradient flow structure of the porous medium equation. We prove that, for the case of q-Gaussians on the real line, the functional derived by the JKO-discretization scheme is asymptotically equivalent to a rate-large-deviation-like functional. The result explains why the Wasserstein metric as well as the combination(More)