Institut Élie Cartan de Lorraine

About: Institut Élie Cartan de Lorraine is a facility organization based out in Vandœuvre-lès-Nancy, France. It is known for research contribution in the topics: Boundary value problem & Stochastic differential equation. The organization has 345 authors who have published 1084 publications receiving 15512 citations. The organization is also known as: Institut Élie-Cartan de Nancy.

Simulation of a diffusion process by using the importance sampling paradigm

Abstract: We construct in this paper a Monte Carlo method in order to approach solutions of multi-dimensional Stochastic Differential Equations processes which relies on the importance sampling technique. Our method is based on the random walk on squares/rectangles method and the main interest of this construction is that the weights are easily computed from the density of the one-dimensional Brownian motion. The advantage we take on the Euler scheme is that this method allows us to get a better simulation of diffusions when one has really to take care of the boundary conditions. Moreover, it provides a good alternative to perform variance reduction techniques and simulation of rare events.

Homotopes of Symmetric Spaces II. Structure Variety and Classification

Abstract: We classify homotopes of classical symmetric spaces (studied in Part I of this work) Our classification uses the fibered structure of homotopes: they are fibered as symmetric spaces, with flat fibers, over a non-degenerate base; the base spaces correspond to inner ideals in Jordan pairs Using that inner ideals in classical Jordan pairs are always complemented (in the sense defined by O Loos and E Neher), the classification of homotopes is obtained by combining the classification of inner ideals with the one of isotopes of a given inner ideal

An optimized Schwarz domain decomposition method with cross-point treatment for time-harmonic acoustic scattering

Abstract: The parallel finite-element solution of large-scale time-harmonic wave problems is addressed with a non-overlapping optimized Schwarz domain decomposition method (DDM). It is well-known that the efficiency of this kind of method strongly depends on the transmission condition enforced on the interfaces between the subdomains. Local conditions based on high-order absorbing boundary conditions (HABCs) have proved to be well-suited, as a good compromise between basic impedance conditions, which lead to suboptimal convergence , and conditions based on the exact Dirichlet-to-Neumann (DtN) map related to the complementary of the subdomain-which are too expensive to compute. However, a direct application of the approach for configurations with interior cross-points (where more than two subdomains meet) and boundary cross-points (points that belong to both the exterior boundary and at least two subdomains) is suboptimal and, in some cases, can lead to incorrect results. In this work, we extend a non-overlapping DDM with HABC-based transmission conditions approach to efficiently deal with cross-points for lattice-type partitioning. The proposed cross-point treatment relies on corner conditions developed for Pade-type HABCs. Two-dimensional numerical results with a nodal finite-element discretization are proposed to validate the approach, including convergence studies with respect to the frequency, the mesh size and the number of subdomains. These results demonstrate the efficiency for settings with regular partitions and homogeneous media. Numerical experiments with non-regular partitions and smoothly varying heterogeneous media show the robustness of the approach.

Convergence of Wigner integrals to the tetilla law

Abstract: If x and y are two free semicircular random variables in a non-commutative probability space (A,E) and have variance one, we call the law of 2^{-1/2}(xy+yx) the tetilla law (and we denote it by T), because of the similarity between the form of its density and the shape of the tetilla cheese from Galicia. In this paper, we prove that a unit-variance sequence {F_n} of multiple Wigner integrals converges in distribution to T if and only if E[F_n^4]--> E[T^4] and E[F_n^6]--> E[T^6]. This result should be compared with limit theorems of the same flavor, recently obtained by Kemp, Nourdin, Peccati & Speicher and Nourdin & Peccati.

Kaleidoscopic groups: permutation groups constructed from dendrite homeomorphisms

Abstract: Given a transitive permutation group, a fundamental object for studying its higher transitivity properties is the permutation action of its isotropy subgroup. We reverse this relationship and introduce a universal construction of infinite permutation groups that takes as input a given system of imprimitivity for its isotropy subgroup. This produces vast families kaleidoscopic groups. We investigate their algebraic properties, such as simplicity and oligomorphy; their homological properties, such as acyclicity or contrariwise large Schur multipliers; their topological properties, such as unique polishability. Our construction is carried out within the framework of homeomorphism groups of topological dendrites.