Showing papers by "Paris West University Nanterre La Défense published in 1989"
TL;DR: In this paper, it was shown that the conditional law of the empirical field given by random Gibbs measures with random interaction satisfies large deviation inequalities, and that the pressure is non-random, and is given by a variational formula.
Abstract: Let (X
i
,Y
i
) ∈ℤ
d
, be independent identically distributed random variables with arbitrary distribution. We show that, for almost every(Y
i
)
i
, the conditional law of the empirical field given(Y
i
)
i
satisfies to large deviation inequalities. This applies to the study of Gibbs measures with random interaction, in the case of some mean-field models as well as of short range summable interaction. We show that the pressure is nonrandom, and is given by a variational formula. These random Gibbs measures have the same large deviation rate, which does not depend on the particular realization of the interaction; their local behaviour is described in terms of conditional probabilities given the interaction of solutions to the variational formula.
74 citations
Patent•
21 Mar 1989TL;DR: In this paper, a convergent lens is used for forming a diffraction pattern of the cloud of particles or of the surface, and a multiplier is used to multiply this pattern, in intensity, by a function f(r) such that A(r.sup.5 + Br.sub.o.1.4)
Abstract: The invention relates to the measurement of the granulometry of a cloud of particles or of the roughness of a surface in real time and without contact, by means of an apparatus comprising: a convergent lens (9) adapted for forming a diffraction pattern of the cloud of particles or of the surface: multiplier means (10) adatped for multiplying this diffraction pattern, in intensity, by a function f(r) such that A(r.sup.1.5 +Br.sub.o.sup.4)
4 citations
TL;DR: A continuous excess demand function is non-positive for some semi-positive price vector, as soon as all commodities cannot be simultaneously in excess demand as discussed by the authors, i.e., all commodities are simultaneously in negative demand.
4 citations
2 citations
TL;DR: It is proved that the languages associated to Vector Addition System or Petri nets have rational indexes bounded by polynomials, and an upper bound and a lower bound on the rational index of each term of an infinite sequence of V.A.S.
Abstract: The rational index ρL of a non-empty language L is a function of ℕ into ℕ, whose asymptotic behavior can be used to classify languages. We prove that the languages associated to Vector Addition System or Petri nets have rational indexes bounded by polynomials. This situation should be contrasted with the case of context-free languages. Indeed some context-free languages like the Greibach's languages have rational indexes bounded by polynomials. But some other context-free languages have rational indexes in exp Θ n and the generators of the rational cone of context-free languages have rational indexes in exp Θ n2/ln n. We give an upper bound and a lower bound on the rational index of each term of an infinite sequence of V.A.S. languages, such that any V.A.S. language can be obtained as the image by a rational transduction of one of these languages.
TL;DR: The relevance of the concept of equilibrium in dealing with the traditional question of the working of the market, the central institution in our economies is discussed in this article, where the authors focus on the importance of the equilibrium concept in the context of economic theory.
Abstract: Economic theory has undergone a very deep transformation during the last forty years. Its method and its tools of analysis have evolved dramatically. The standards by which theoretical statements are now appreciated are far more demanding, especially from a formal point of view, than was the case before World War II. Precision and logical validity in raising questions and problems have increased as well. The set of hypotheses necessary to deal with the usual issues of political economy has been made more explicit, allowing everyone to have a more clearer interpretation of what has been done in the different fields. The content and the relevance of the concept of equilibrium have been strongly affected by these transformations. This paper, obviously, does not attempt to give an account of all these changes. It will focus on just one consequence of this evolution: the relevance of the concept of equilibrium in dealing with the traditional question of the working of the market, the central institution in our economies. To put the matter very briefly, the question addressed here concerns the place of equilibrium in economic theory: does mainstream economics allow for another theoretical reference? For two centuries at least, equilibrium was referred to as a particular situation towards which the market mechanism was supposed to drive the economy. An important issue was to prove this conjecture. Whereas mainstream economists (Smith, Ricardo, Stuart Mill, Marshall and Walras) endeavoured to prove the stability of the market, critical authors tried to show that certain fundamental flaws of the market mechanism make instability and crisis the rule in a capitalist economy. Among the factors said to be responsible for this result, the monetary character of the economy seems the most important (as was emphasized by Boisguilbert, Sismondi and Marx in the past and by Keynes in our time).