Limiting laws associated with Brownian motion perturbed by its maximum, minmum and local time II

We obtain probability measures on the canonical space penalizing the Wiener measure by a function of its maximum (resp. minimum, local time). We study the law of the canonical process under these new probability measures

BRST cohomology of the Chapline-Manton model

We completely compute the local BRST cohomology $H(s|d)$ of the combined Yang-Mills-2-form system coupled through the Yang-Mills Chern-Simons term ("Chapline-Manton model"). We consider the case of a simple gauge group and explicitely include in the analysis the sources for the BRST variations of the fields ("antifields"). We show that there is an antifield independent representative in each cohomological class of $H(s|d)$ at ghost number 0 or 1. Accordingly, any counterterm may be assumed to preserve the gauge symmetries. Similarly, there is no new candidate anomaly beside those already considered in the literature, even when one takes the antifields into account. We then characterize explicitly all the non-trivial solutions of the Wess-Zumino consistency conditions. In particular, we provide a cohomological interpretation of the Green-Schwarz anomaly cancellation mechanism.Comment: Latex file, no figures, 15 page

A global view of Brownian penalisations

In this monograph, we construct and study a sigma-finite measure on continuous functions from R_+ to R, strongly related to many probability measures obtained by penalisation of Brownian motion, i.e. as limits of probabilities which are absolutely continuous with respect to Wiener measure. This remarkable sigma-finite measure can be generalized in three other cases: one can start from a two-dimensional Brownian motion, from a recurrent diffusion with values in R_+, and from a discrete, recurrent Markov chain

Limiting laws associated with Brownian motion perturbated by normalized exponential weights I

We determine the rate of decay of the expectation Z(t) of some multiplicative functional related to Brownian motion up to time t. This permits to prove that the Wiener measure, penalized by this multiplicative functional, converges as t goes to infinity to a probability measure (p.m.) . We obtain the law of the canonical process under this new p.m

How can countries use cross-national research results to address "the big policy issues" ? (Case studies from Francophone Africa)

The “Program on the Analysis of Education Systems“ (PASEC) was launched in 1991 at the conference of francophone education ministers (CONFEMEN) in Djibouti and carried out its first country evaluation one year later in the same country. Since then, 13 individual country evaluations have been carried out in francophone sub-Saharan Africa, including panel studies following primary students from 2nd to 6th grade within a given country. The primary objective of PASEC evaluations is not the comparison of student achievement across countries, but the analysis of key factors relevant to foster educational quality. Created at the initiative of education ministers with the clear objective to inform educational decision making, the translation of PASEC results into actual education policy has yet not been automatic. This paper will discuss specific procedures and measures adopted in order to ensure that PASEC results are actually taken into account by policy makers and other target groups within the education sector. Moreover, this paper will illustrate to what extent PASEC has already contributed to concrete educational policy reform.Cross-national studies ; Educational quality ; Educational policy ; Subsaharan Africa

Existence of Equilibria with a Tight Marginal Pricing Rule.

This paper deals with the existence of marginal pricing equilibria when it is defined by using a new and tighter normal cone introducedby B. Cornet and M.O. Czarnecki. The main interest of this new definition of the marginal pricing rule comes from the fact that it is more precise in the sense that the set of prices satisfying the condition is smaller than the one given by the Clarke's normal cone. The counter- part is that it is not convex valued, which leads to some mathematical diffculties in the existence proof. The result is obtained through an approximation argument under the same assumptions as in the previous existence results.General economic equilibrium, increasing returns, marginal pricing rule, existence.

E11E_{11}, Borcherds algebras and maximal supergravity

The dynamical $p$-forms of torus reductions of maximal supergravity theory have been shown some time ago to possess remarkable algebraic structures. The set ("dynamical spectrum") of propagating $p$-forms has been described as a (truncation of a) real Borcherds superalgebra \mf{V}_D that is characterized concisely by a Cartan matrix which has been constructed explicitly for each spacetime dimension $11 \geq D \geq 3.$ In the equations of motion, each differential form of degree $p$ is the coefficient of a (super-) group generator, which is itself of degree $p$ for a specific gradation (the \mf{V}-gradation). A slightly milder truncation of the Borcherds superalgebra enables one to predict also the "spectrum" of the non-dynamical $(D - 1)$ and $D$-forms. The maximal supergravity $p$-form spectra were reanalyzed more recently by truncation of the field spectrum of $E_{11}$ to the $p$-forms that are relevant after reduction from 11 to $D$ dimensions. We show in this paper how the Borcherds description can be systematically derived from the split ("maximally non compact") real form of $E_{11}$ for $D \geq 1.$ This explains not only why both structures lead to the same propagating $p$-forms and their duals for $p\leq (D - 2),$ but also why one obtains the same $(D - 1)$-forms and "top" $D$-forms. The Borcherds symmetries \mf{V}_2 and \mf{V}_1 are new too. We also introduce and use the concept of a presentation of a Lie algebra that is covariant under a given subalgebra.Comment: 39 pages. Version 2 contains improved presentation in particular an extra appendix B giving details on the infinite rank limit possibility. Version to appear in JHE

Generalized Gamma Convolutions, Dirichlet means, Thorin measures, with explicit examples

In Section 1, we present a number of classical results concerning the Generalized Gamma Convolution (:GGC) variables, their Wiener-Gamma representations, and relation with the Dirichlet processes.To a GGC variable, one may associate a unique Thorin measure. Let $G$ a positive r.v. and $\Gamma_t(G)$ (resp. $\Gamma_t(1/G))$ the Generalized Gamma Convolution with Thorin measure $t$-times the law of $G$ (resp. the law of $1/G$). In Section 2, we compare the laws of $\Gamma_t(G)$ and $\Gamma_t(1/G)$.In Section 3, we present some old and some new examples of GGC variables, among which the lengths of excursions of Bessel processes straddling an independent exponential time.Comment: Published in at http://dx.doi.org/10.1214/07-PS118 the Probability Surveys (http://www.i-journals.org/ps/) by the Institute of Mathematical Statistics (http://www.imstat.org