Paris Dauphine University

About: Paris Dauphine University is a education organization based out in Paris, France. It is known for research contribution in the topics: Context (language use) & Population. The organization has 1766 authors who have published 6909 publications receiving 162747 citations. The organization is also known as: Paris Dauphine & Dauphine.

Full well-posedness of point vortex dynamics corresponding to stochastic 2D Euler equations

Abstract: The motion of a finite number of point vortices on a two-dimensional periodic domain is considered. In the deterministic case it is known to be well posed only for almost every initial configuration. Coalescence of vortices may occur for certain initial conditions. We prove that when a generic stochastic perturbation compatible with the Eulerian description is introduced, the point vortex motion becomes well posed for every initial configuration, in particular coalescence disappears.

Long time semiclassical approximation of quantum flows: A proof of the Ehrenfest time

Abstract: Let H be a holomorphic Hamiltonian of quadratic growth on R, b a holomorphic exponentially localized observable, H ,B the corresponding operators on L(R) generated by Weyl quantization, and U (t) = exp iHt/~. It is proved that the L norm of the difference between the Heisenberg observable Bt = U (t)BU (−t) and its semiclassical approximation of order N −1 is majorized by KN (6n+1)N~−4/9(−~ log ~) for t ∈ [0,Tn(~)], where Tn(~) := −2 log ~/[α(6n+ 3)(N −1)] and α := ‖Hess(x,ξ)H‖. Choosing a suitable N(~) the error is majorized by C~ | log ~|, 0 6 t 6 | log ~|/ log | log ~| (here K and C are explicit constants independent of N , ~).

Monotonically convergent optimal control theory of quantum systems with spectral constraints on the control field

Abstract: We propose a monotonically convergent algorithm which can enforce spectral constraints on the control field (and extends to arbitrary filters). The procedure differs from standard algorithms in that at each iteration, the control field is taken as a linear combination of the control field (computed by the standard algorithm) and the filtered field. The parameter of the linear combination is chosen to respect the monotonic behavior of the algorithm and to be as close to the filtered field as possible. We test the efficiency of this method on molecular alignment. Using bandpass filters, we show how to select particular rotational transitions to reach high alignment efficiency. We also consider spectral constraints corresponding to experimental conditions using pulse-shaping techniques. We determine an optimal solution that could be implemented experimentally with this technique.

Sampling from a Log-Concave Distribution with Projected Langevin Monte Carlo

Abstract: We extend the Langevin Monte Carlo (LMC) algorithm to compactly supported measures via a projection step, akin to projected Stochastic Gradient Descent (SGD). We show that (projected) LMC allows to sample in polynomial time from a log-concave distribution with smooth potential. This gives a new Markov chain to sample from a log-concave distribution. Our main result shows in particular that when the target distribution is uniform, LMC mixes in O(n 7) steps (where n is the dimension). We also provide preliminary experimental evidence that LMC performs at least as well as hit-and-run, for which a better mixing time of O(n 4) was proved by Lovasz and Vempala.