A Renewal Theorem for Strongly Ergodic Markov Chains in Dimension d≥3d\geq3 and Centered Case

In dimension $d\geq3$, we present a general assumption under which the renewal theorem established by Spitzer for i.i.d. sequences of centered nonlattice r.v. holds true. Next we appeal to an operator-type procedure to investigate the Markov case. Such a spectral approach has been already developed by Babillot, but the weak perturbation theorem of Keller and Liverani enables us to greatly weaken thehypotheses in terms of moment conditions. Our applications concern the v$-geometrically ergodic Markov chains, the$\rho$-mixing Markov chains, and the iterative Lipschitz models, for which the renewal theorem of the i.i.d. case extends under the (almost) expected moment condition

Restaurant Prices and the Minimum Wage

We examine the effect of the minimum wage on restaurant prices. We contribute to both the study of economic impact of the minimum wage and to the micro patterns of price stickiness. For that purpose, we use a unique dataset of individual price quotes collected to calculate the Consumer Price Index in France and we estimate a price rigidity model based on a flexible (S; s) rule. We find a positive and significant impact of the minimum wage on prices. The effect of the minimum wage on prices is however very protracted. The aggregate impact estimated with our model takes more than a year to fully pass through to retail prices.price stickiness, minimum wage, inflation, restaurant prices

A physics-based approach to flow control using system identification

Control of amplifier flows poses a great challenge, since the influence of environmental noise sources and measurement contamination is a crucial component in the design of models and the subsequent performance of the controller. A modelbased approach that makes a priori assumptions on the noise characteristics often yields unsatisfactory results when the true noise environment is different from the assumed one. An alternative approach is proposed that consists of a data-based systemidentification technique for modelling the flow; it avoids the model-based shortcomings by directly incorporating noise influences into an auto-regressive (ARMAX) design. This technique is applied to flow over a backward-facing step, a typical example of a noise-amplifier flow. Physical insight into the specifics of the flow is used to interpret and tailor the various terms of the auto-regressive model. The designed compensator shows an impressive performance as well as a remarkable robustness to increased noise levels and to off-design operating conditions. Owing to its reliance on only timesequences of observable data, the proposed technique should be attractive in the design of control strategies directly from experimental data and should result in effective compensators that maintain performance in a realistic disturbance environment

Atomic-like spin noise in solid-state demonstrated with manganese in cadmium telluride

Spin noise spectroscopy is an optical technique which can probe spin resonances non-perturbatively. First applied to atomic vapours, it revealed detailed information about nuclear magnetism and the hyperfine interaction. In solids, this approach has been limited to carriers in semiconductor heterostructures. Here we show that atomic-like spin fluctuations of Mn ions diluted in CdT e (bulk and quantum wells) can be detected through the Kerr rotation associated to excitonic transitions. Zeeman transitions within and between hyperfine multiplets are clearly observed in zero and small magnetic fields and reveal the local symmetry because of crystal field and strain. The linewidths of these resonances are close to the dipolar limit. The sensitivity is high enough to open the way towards the detection of a few spins in systems where the decoherence due to nuclear spins can be suppressed by isotopic enrichment, and towards spin resonance microscopy with important applications in biology and materials science

Multidimensional renewal theory in the non-centered case. Application to strongly ergodic Markov chains.

International audienceLet $(S_n)_n$ be a $R^d$-valued random walk ($d\geq2$). Using Babillot's method [2], we give general conditions on the characteristic function of $S_n$ under which $(S_n)_n$ satisfies the same renewal theorem as the classical one obtained for random walks with i.i.d. non-centered increments. This statement is applied to additive functionals of strongly ergodic Markov chains under the non-lattice condition and (almost) optimal moment conditions

Heat Estimation from Infrared Measurement Compared to DSC for Austenite to R Phase Transformation in a NiTi Alloy

International audienceHeat sources estimations from temperature field measurements deduced from infrared imaging are increasingly used to study thermo-mechanical coupling during materials deformation. These estimations are based on approximations of the derivative terms with respect to time and space which are involved in the heat diffusion equation. This paper proposes a first experimental validation of this method by applying it to an experimental uniform air cooling of a NiTi Shape Memory Alloy thin plate. In the studied cooling temperate range, heat sources are due to Austenite to R phase transformation. Transformation temperatures, heat sources and energies are estimated from infrared temperature measurements and compared to differential scanning calorimetry results. The small 2 discrepancies are mainly explained by errors in DSC measurements due to thermal inertia and baseline determination

Medical ultrasound image reconstruction using distributed compressive sampling

International audienceThis paper investigates ultrasound (US) radiofrequency (RF) signal recovery using the distributed compressed sampling framework. The “correlation” between the RF signals forming a RF image is exploited by assuming that they have the same sparse support in the 1D Fourier transform, with different coefficient values. The method is evaluated using an experimental US image. The results obtained are shown to improve a previously proposed recovery method, where the correlation between RF signals was taken into account by assuming the 2D Fourier transform of the RF image sparse

Sub-Gap Structure in the Conductance of a Three-Terminal Josephson Junction

Three-terminal superconductor (S) - normal metal (N) - superconductor (S) Josephson junctions are investigated. In a geometry where a T-shape normal metal is connected to three superconducting reservoirs, new sub-gap structures appear in the differential resistance for specific combinations of the superconductor chemical potentials. Those correspond to a correlated motion of Cooper pairs within the device that persist well above the Thouless energy and is consistent with the prediction of quartets formed by two entangled Cooper pairs. A simplified nonequilibrium Keldysh Green's function calculation is presented that supports this interpretation.Comment: To appear in Physical Review

Quasi-compactness of Markov kernels on weighted-supremum spaces and geometrical ergodicity

Let $P$ be a Markov kernel on a measurable space \X and let V:\X\r[1,+\infty). We provide various assumptions, based on drift conditions, under which $P$ is quasi-compact on the weighted-supremum Banach space (\cB_V,\|\cdot\|_V) of all the measurable functions f : \X\r\C such that \|f\|_V := \sup_{x\in \X} |f(x)|/V(x) < \infty. Furthermore we give bounds for the essential spectral radius of $P$. Under additional assumptions, these results allow us to derive the convergence rate of $P$ on \cB_V, that is the geometric rate of convergence of the iterates $P^n$ to the stationary distribution in operator norm. Applications to discrete Markov kernels and to iterated function systems are presented.Comment: 45 page