Semiclassical Resonances of Schr\"odinger operators as zeroes of regularized determinants

We prove that the resonances of long range perturbations of the (semiclassical) Laplacian are the zeroes of natural perturbation determinants. We more precisely obtain factorizations of these determinants of the form $\prod_{w = {\rm resonances}}(z-w) \exp (\varphi_p(z,h))$ and give semiclassical bounds on $\partial_z \varphi_p$ as well as a representation of Koplienko's regularized spectral shift function. Here the index $p \geq 1$ depends on the decay rate at infinity of the perturbation.Comment: 37 pages, published versio

Payoff-dependent balancedness and cores (revised version)

We prove the non-emptiness of the core of an NTU game satisfying a condition of payoff-dependent balancedness, based on transfer rate mappings. We also define a new equilibrium condition on transfer rates and we prove the existence of core payoff vectors satisfying this condition. The additional requirement of transfer rate equilibrium refines the core concept and allows the selection of specific core payoff vectors. Lastly, the class of parametrized cooperative games is introduced. This new setting and its associated equilibrium-core solution extend the usual cooperative game framework and core solution to situations depending on an exogenous environment. A non-emptiness result for the equilibrium-core is also provided in the context of a parametrized cooperative game. Our proofs borrow mathematical tools and geometric constructions from general equilibrium theory with non convexities. Applications to extant results taken from game theory and economic theory are given.balancedness, cooperative game, core, parametrized game

Payoff-dependant Balancedness and Cores.

We prove the non-emptiness of the core of an NTU game satisfying a condition of payoff-dependent balancedness, based on transfer rate mappings. We also define a new equilibrium condition on transfer rates and we prove the existence of core payoff vectors satisfying this condition. The additional requirement of transfer rate equilibrium refines the core concept and allows the selection of specific core payoff vectors. Lastly, the class of parameterized cooperative games is introduced. This new setting and its associated equilibrium–core solution extend the usual cooperative game framework and core solution to situations depending on an exogenous environment. A non-emptiness result for the equilibrium–core is also provided in the context of a parametrized cooperative game. Our proofs borrow mathematical tools and geometric constructions from general equilibrium theory with non-convexities. Applications to extant results taken from game theory and economic theory are given.Balancedness; Cooperative game; Core; Parametrized game;

Payoffs-dependent Balancedness and Cores

We provide a result for non-emptiness of the core in NTU games. We use a payoffs-dependent balancedness condition, based on transfer rate mappings. Going beyond the non-emptiness of standard core, existence of some refined solution is proved, including specific core allocations and equilibrium-core allocations in parameterized collection of cooperative games. The proofs borrow mathematical tools and geometric constructions from general equilibrium theory with non convexities. Applications to various extant results taken from game theory and economic theory are given.Cooperative games, Core solutions, Non-emptiness

Inverse participation ratios in the XXZ spin chain

We investigate numerically the inverse participation ratios in a spin-1/2 XXZ chain, computed in the "Ising" basis (i.e., eigenstates of $\sigma^z_i$). We consider in particular a quantity $T$, defined by summing the inverse participation ratios of all the eigenstates in the zero magnetization sector of a finite chain of length $N$, with open boundary conditions. From a dynamical point of view, $T$ is proportional to the stationary return probability to an initial basis state, averaged over all the basis states (initial conditions). We find that $T$ exhibits an exponential growth, $T\sim\exp(aN)$, in the gapped phase of the model and a linear scaling, $T\sim N$, in the gapless phase. These two different behaviors are analyzed in terms of the distribution of the participation ratios of individual eigenstates. We also investigate the effect of next-nearest-neighbor interactions, which break the integrability of the model. Although the massive phase of the non-integrable model also has $T\sim\exp(aN)$, in the gapless phase $T$ appears to saturate to a constant value.Comment: 8 pages, 7 figures. v2: published version (one figure and 3 references added, several minor changes

Perfect simulation, monotonicity and finite queueing networks

International audienceTutorial on perfect sampling with applications to queueing network

Wake instabilities behind an axisymmetric bluff body at low Reynolds numbers

This paper aims at understanding the dynamical process that leads to the onset of chaos in the flow past a blunt based axisymmetric bluff body. On the ba- sis of direct numerical simulations, conducted for Reynolds numbers ranging from 100 to 800, we show that the flow undergoes multiple transitions, successively giv- ing rise to the SS, RSPa, RSPb and RSPc wake states. In particular, the RSPc state, revealed in this work via long-term computations, is characterized by intermittent vortex stretching denoting the onset of chaos and the potential occurence of a third instability that superimposes to the first and second instability associated with state RSPa and RSPb respectively. Interestingly, the reflectional symmetry plane that characterizes the RSP states is still retained. Hence, chaos is triggered before the symmetry breaking and the occurence of the RSB state observed at higher Reynolds numbers

Les Bas-Champs de Cayeux (Somme, France) : vers une gestion intégrée ? Enjeux et perspectives de l'ouverture à la mer d'un espace jusque là protégé

Article accessible en ligne sur le site de VertigO à la page : http://www.vertigo.uqam.ca/vol7no3/framerevue.htmlInternational audienceAbstract : Have the recent public policies for the management of coastal areas impulsed notable changes in projects ? The example studied here tends to prove that a concept (the GIZC), rather new in France, can have some influence on local management of coastal areas if respected in its principles. We shall study a new kind of management in the southern part of the Baie de Somme, on a coastal area where new initiatives have been taken consequently to the decisions taken in the CIADT (interministerial comittees for the territorial management and developpement) in April 2001 and September 2004. There, indeed, the notions of sustainable development and of GIZC have been promoted, belatedly with reference to advice of the Bonnot report (1995), and show the necessity of a proper policy concerning coastal areas, as playing no poor part in the global environmental policy. The « Bas-Champs » of Cayeux is a space demarcated on its eastern boundary by an old cliff and protected from erosion by the waves on its western boundary by a shingle ridge eroded by the waves. The penetration by the tide into this former sea space has been stopped since the « grand barrement » in 1752 (old gravel workings inland ). The struggle against sea action has been lasting for three centuries, in order to protect the land and surrounding fields gained on the sea. These sea defences have been damaged in some places after high tides and strong storms blowing West. The most powerful storm happened in 1990 and led to the flooding of 35 square kilometres of productive farmlands. The cost of works to protect and reinforce the ridge amounts to over 30 M euros, plus 350,000 euros a year for maintenance... which means... ad vitam æternam ? These costs are higher than the economic value of the properties they protect. Thus, allowing the tide to penetrate again into this former sea space migth be a solution in agreement with the principles of the GIZC and the sustainble development.Résumé : Les politiques publiques récentes d'aménagement du territoire consacrées au littoral ont-elles impulsé des changements notables en termes de gestion ? L'exemple étudié ici tend à démontrer qu'un concept relativement nouveau en France, celui de la GIZC, peut, si ses principes sont respectés, influer sur les politiques locales d'aménagement d'un littoral aux enjeux importants mais également en pleine évolution. Nous nous intéresserons à un secteur côtier du sud de la Baie de Somme pour lequel une nouvelle approche se profile en termes d'aménagements. Les décisions prises lors des CIADT (Comités Interministériels pour l'Aménagement et le Développement du Territoire) d'avril 2001 et septembre 2004 n'y sont certainement pas étrangères. C'est là en effet que les notions de développement durable et de GIZC ont été mises en avant, faisant tardivement suite aux recommandations du Rapport Bonnot (1995), et traduisant la nécessité d'avoir une politique du littoral propre, qui ne soit plus portion (souvent congrue) de la politique environnementale globale. Les Bas-Champs de Cayeux, site d'étude, constituent un espace délimité à l'est par une falaise morte et protégé de la mer, sur leur flanc ouest, par un cordon de galets soumis à l'érosion. L'accès de la mer à cet ancien espace maritime, est définitivement clos par « le grand barrement » en 1752. Depuis trois siècles, le combat dure afin de préserver ces terres gagnées sur la mer. Des brèches se sont ouvertes lors de fortes marées concomitantes avec des vents d'ouest soutenus et importants. La tempête la plus importante a eu lieu en 1990 et entraînera l'inondation de 35 km2 de terres cultivables. Le coût des travaux prévus depuis pour maintenir et consolider la digue s'élève à plus de 40 millions d'euros auxquels il convient d'ajouter près de 350 000 euros par an pour l'entretenir... ad vitam aeternam ? Ces coûts sont supérieurs à la valeur économique des biens qu'ils défendent. Ainsi, rouvrir à la mer cet espace ne serait-il pas une solution en adéquation avec les principes de GIZC et de développement durable

On the Voting Power of an Alliance and the Subsequent Power of its Members

Even, and in fact chiefly, if two or more players in a voting gamehave on a binary issue independent opinions, they may haveinterest to form a single voting alliance giving an average gainof influence for all of them. Here, assuming the usualindependence of votes, we first study the alliance voting powerand obtain new results in the so-called asymptotic limit for whichthe number of players is large enough and the alliance weightremains a small fraction of the total of the weights. Then, wepropose to replace the voting game inside the alliance by a randomgame which allows new possibilities. The validity of theasymptotic limit and the possibility of new alliances are examinedby considering the decision process in the Council of Ministers ofthe European Union.Voting Power; Alliance