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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)

- Manh Hong Duong, Vaios Laschos, Michiel Renger
- 2012

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)

- Manh Hong Duong, Han The Anh
- ArXiv
- 2014

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)

- Manh Hong Duong
- 2017

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)

- Mark Peletier, Alex Cox, +4 authors Michiel Renger
- 2013

and Michiel Renger for comments on earlier drafts of these notes.

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)

- Manh Hong Duong
- 2017

Inequalities are ubiquitous in Mathematics (and in real life). For example, in optimization theory (particularly in linear programming) inequalities are used to described constraints. In analysis inequalities are frequently used to derive a priori estimates, to control the errors and to obtain the order of convergence, just to name a few. Of particular… (More)

- Manh Hong Duong
- Asymptotic Analysis
- 2015

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)

- Manh Hong Duong
- 2015

In [2], a new method to study hydrodynamic limits, called the two-scale approach, was developed for reversible dynamics. In this work, we generalize this method to a family of non-reversible dynamics. As an application, we obtain quantitative rates of convergence to the hydrodynamic limit for a weakly asymmetric version of the Ginzburg-Landau model endowed… (More)