Spectral measure and approximation of homogenized coefficients

This article deals with the numerical approximation of effective coefficients in stochastic homogenization of discrete linear elliptic equations. The originality of this work is the use of a well-known abstract spectral representation formula to design and analyze effective and computable approximations of the homogenized coefficients. In particular, we show that information on the edge of the spectrum of the generator of the environment viewed by the particle projected on the local drift yields bounds on the approximation error, and conversely. Combined with results by Otto and the first author in low dimension, and results by the second author in high dimension, this allows us to prove that for any dimension, there exists an explicit numerical strategy to approximate homogenized coefficients which converges at the rate of the central limit theorem.Comment: 30 pages, 2 figure

Quantitative version of the Kipnis-Varadhan theorem and Monte Carlo approximation of homogenized coefficients

This article is devoted to the analysis of a Monte Carlo method to approximate effective coefficients in stochastic homogenization of discrete elliptic equations. We consider the case of independent and identically distributed coefficients, and adopt the point of view of the random walk in a random environment. Given some final time t>0, a natural approximation of the homogenized coefficients is given by the empirical average of the final squared positions re-scaled by t of n independent random walks in n independent environments. Relying on a quantitative version of the Kipnis-Varadhan theorem combined with estimates of spectral exponents obtained by an original combination of PDE arguments and spectral theory, we first give a sharp estimate of the error between the homogenized coefficients and the expectation of the re-scaled final position of the random walk in terms of t. We then complete the error analysis by quantifying the fluctuations of the empirical average in terms of n and t, and prove a large-deviation estimate, as well as a central limit theorem. Our estimates are optimal, up to a logarithmic correction in dimension 2.Comment: Published in at http://dx.doi.org/10.1214/12-AAP880 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Quantum gauge theories on noncommutative 3-d space

We consider a class of gauge invariant models on the noncommutative space $\mathbb{R}^3_\lambda$, a deformation of $\mathbb{R}^3$. Focusing on massless models with no linear $A_i$ dependence, we obtain noncommutative gauge models for which the computation of the propagator can be done in a convenient gauge. We find that the infrared singularity of the massless propagator disappears in the computation of the correlation functions. We show that massless gauge invariant models on $\mathbb{R}^3_\lambda$ have quantum instabilities of the vacuum, signaled by the occurrence of non vanishing 1-point functions for some but not all of the components of the gauge potential. The tadpole contribution to the effective action cannot be interpreted as a standard $\sigma$-term. Its global symmetry does not fit with the one of the classical action, reminiscent to an explicit global symmetry breaking term.Comment: 31 pages. Section 2 modified with two new subsections about derivations of the algebra and the integration measure. References adde

Multilateral agricultural trade liberalization: The contrasting fortunes of developing countries in the Doha Round

An applied general equilibrium model is used to assess the impact of multilateral trade liberalization in agriculture, with particular emphasis on developing countries. We use original data, and the model includes some specific features such as a dual labor market. Applied tariffs, including those under preferential regimes and regional agreements, are taken into account at the detailed product level, together with the corresponding bound tariffs on which countries negotiate. The various types of farm support are detailed, and several groups of developing countries are distinguished. Simulations give a contrasted picture of the benefits developing countries would draw from the Doha development round. The results suggest that previous studies that have neglected preferential agreements and the binding overhang (in tariffs as well as domestic support), and have treated developed countries with a high level of aggregation have been excessively optimistic about the actual benefits of multilateral trade liberalization. Regions like sub-Saharan Africa are more likely to suffer from the erosion of existing preferences. The main gainers of the Doha round are likely to be developed countries and Cairns group members. Classification-CGE model, Doha Round, agriculture, tariff preferences, domestic support.

Multiplayer belief revision

One main topic of the epistemic program of game theory deals with the value of information. To study this question in a broad context, one needs to adapt some of the tools used in multiplayer epistemic logic. A hierarchical belief structure is introduced both in a syntactical and semantical framework. In the same framework, a generalized notion of message is characterized by its content and its status. For a given message, a multiplayer belief revision rule that transforms any initial belief structure into a final belief one is designed. A representation theorem relates syntactical axioms to the belief revision rule.Belief revision, message, epistemic logic.

Polaritonic modes in a dense cloud of atoms

We analyze resonant light scattering by an atomic cloud in a regime where near-field interactions between scatterers cannot be neglected. We first use a microscopic approach and calculate numerically the eigenmodes of the cloud for many different realizations. It is found that there always exists a small number of polaritonic modes that are spatially coherent and superradiant. We show that scattering is always dominated by these modes. We then use a macroscopic approach by introducing an effective permittivity so that the atomic cloud is equivalent to a dielectric particle. We show that there is a one-to-one correspondence between the microscopic polaritonic modes and the modes of a homogeneous particle with an effective permittivity

Multiplayer belief revision

URL des Documents de travail : http://ces.univ-paris1.fr/cesdp/CESFramDP2008.htmClassification JEL : C72, D82.Documents de travail du Centre d'Economie de la Sorbonne 2008.67 - ISSN : 1955-611XOne main topic of the epistemic program of game theory deals with the value of information. To study this question in a broad context, one needs to adapt some of the tools used in multiplayer epistemic logic. A hierarchical belief structure is introduced both in a syntactical and semantical framework. In the same framework, a generalized notion of message is characterized by its content and its status. For a given message, a multiplayer belief revision rule that transforms any initial belief structure into a final belief one is designed. A representation theorem relates syntactical axioms to the belief revision rule.Cet article traite de la révision des croyances dans un cadre multi-agents. Il propose une formalisation de l'arrivée d'information apportée par un message. Dans un cadre sémantique, nous proposons une règle de révision des croyances dont nous donnons les fondements axiomatiques exprimés dans un cadre syntaxique