Manh Hong Duong

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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 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 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)
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