Coalescent tree based functional representations for some Feynman-Kac particle models

We design a theoretic tree-based functional representation of a class of Feynman-Kac particle distributions, including an extension of the Wick product formula to interacting particle systems. These weak expansions rely on an original combinatorial, and permutation group analysis of a special class of forests. They provide refined non asymptotic propagation of chaos type properties, as well as sharp \LL\_p-mean error bounds, and laws of large numbers for $U$-statistics. Applications to particle interpretations of the top eigenvalues, and the ground states of Schr\"{o}dinger semigroups are also discussed

On the quantization of polygon spaces

Moduli spaces of polygons have been studied since the nineties for their topological and symplectic properties. Under generic assumptions, these are symplectic manifolds with natural global action-angle coordinates. This paper is concerned with the quantization of these manifolds and of their action coordinates. Applying the geometric quantization procedure, one is lead to consider invariant subspaces of a tensor product of irreducible representations of SU(2). These quantum spaces admit natural sets of commuting observables. We prove that these operators form a semi-classical integrable system, in the sense that they are Toeplitz operators with principal symbol the square of the action coordinates. As a consequence, the quantum spaces admit bases whose vectors concentrate on the Lagrangian submanifolds of constant action. The coefficients of the change of basis matrices can be estimated in terms of geometric quantities. We recover this way the already known asymptotics of the classical 6j-symbols

International Navigation Market

Economic record of human society in the last period has involved an unprecedented growth of world trade, trafficking of basic raw materials needed for industry and agriculture, and trade in industrial products or food. To the huge volume of movement of goods, shipping takes back the role of first order both quantitatively as well as efficiency. This situation is encouraged by factors such as diversification of trade, number of participants in this process and the increasingly complex international trade

International Navigation Market

Economic record of human society in the last period has involved an unprecedented growth of world trade, trafficking of basic raw materials needed for industry and agriculture, and trade in industrial products or food. To the huge volume of movement of goods, shipping takes back the role of first order both quantitatively as well as efficiency. This situation is encouraged by factors such as diversification of trade, number of participants in this process and the increasingly complex international trade