Asymptotics of Hankel determinants with a one-cut regular potential and Fisher-Hartwig singularities

We obtain asymptotics of large Hankel determinants whose weight depends on a one-cut regular potential and any number of Fisher-Hartwig singularities. This generalises two results: 1) a result of Berestycki, Webb and Wong [5] for root-type singularities, and 2) a result of Its and Krasovsky [37] for a Gaussian weight with a single jump-type singularity. We show that when we apply a piecewise constant thinning on the eigenvalues of a random Hermitian matrix drawn from a one-cut regular ensemble, the gap probability in the thinned spectrum, as well as correlations of the characteristic polynomial of the associated conditional point process, can be expressed in terms of these determinants.Comment: 41 pages, 4 figure

Asymptotics for Toeplitz determinants: perturbation of symbols with a gap

We study the determinants of Toeplitz matrices as the size of the matrices tends to infinity, in the particular case where the symbol has two jump discontinuities and tends to zero on an arc of the unit circle at a sufficiently fast rate. We generalize an asymptotic expansion by Widom [22], which was known for symbols supported on an arc. We highlight applications of our results in the Circular Unitary Ensemble and in the study of Fredholm determinants associated to the sine kernel.Comment: 28 pages, 5 figure

Traceability, Trust and Coordination in a Food Chain

In response to sanitary crisis, risk management has become a central issue for food producers and distributors in Europe. Organisational responses to sanitary risks usually implying traceability have been conceived by firms. One of the main tasks here is to deal with coordination of the different operators of a food chain. The European Union has developed a regulatory framework with the Regulation 178/2002. This regulation sets a mandatory traceability considered as a risk management tool. Traceability that was considered as a private initiative has therefore become an obligation with this regulation. This paper tries to evaluate if the problem of the operators coordination on specific traceability practices that any private organisational of a food chain had to face is solved with the strict application of the Regulation 178/2002. For that, the analysis characterises the mandatory traceability and the operators responsibilities set by the regulation. The coordination task and the problem of trust that it contains is then described. The analysis shows the limits of the mandatory traceability in this context and suggests a solution.traceability, risk management, food safety, Agribusiness, Industrial Organization, I18, K32, Q18.,

Importance and Limits of the Cost-Benefit Analysis for GMOs Regulation

New technologies and innovations suspected to affect environment or public health need to be regulated. Scientific risk assessment is considered as a key element for the regulation. Its role is reinforced when the regulation has the potential of constraining the international trade. The Sanitary and Phytosanitary Agreement of the WTO dealing with this kind of issues gives primacy to scientific risk assessment. Interesting situations arise with small risks that is to say situations where the probability of damage is tiny and/or expected damages are very small. If risk assessment is the only scientific element considered, the mere presence of risk – even small - should give reason for regulation. Does it rationalize the public decision for all that? If the social benefits associated with the blocked activity are consequent accepting the risk could be worthwhile. Recent works from the economic literature have shown that in order to get a good ‘risk governance’ cost-benefit analysis should be considered together with risk assessment (Bureau et al. 1998, Turvey and Mojduszka 2005). The aim of cost-benefit analysis is indeed to help public decision making. It consists in a set of methods that enables to evaluate the relevance of a regulation, comparing it with other possible options (from other types of regulation to the absence of any regulation). For that purpose cost-benefit analysis aims at estimating a monetary valuation, on the one hand, for environmental (or public health) degradation and, on the other hand, for the expected benefits implied by environmental conservation and technologies’ development.Agribusiness, Agricultural and Food Policy, Farm Management, Food Consumption/Nutrition/Food Safety, Industrial Organization,

Food Safety, Market Power and Private Standards. An Analysis of the Emerging Strategies of Food Operators

The European Union has developed a regulatory framework on food safety with the European Regulation 178/2002. Simultaneously growing consumers’ exigencies on food safety can be perceived. The European Regulation 178/2002 sets rules and procedures in the matter of food safety that, in many aspects, are novelties. The operators’ responsibilities and the mandatory traceability set by this regulation and put into practice since January 2005 are good examples of these regulatory innovations. These dispositions have important implications on the practices developed to ascertain food safety. The ‘traditional’ procedures indeed have been judged insufficient in front of the new regulatory exigencies.Agribusiness, Food Consumption/Nutrition/Food Safety,

Klein tunneling and electron optics in Dirac-Weyl fermion systems with tilted energy dispersion

The outstanding electronic properties of relativistic-like fermions have been extensively studied in solid state systems with isotropic linear dispersions such as graphene. Here, we show that 2D and 3D Dirac-Weyl (DW) materials exhibiting tilted energy dispersions could induce drastically different transport phenomena, compared to the non-tilted case. Indeed, the Klein tunneling of DW fermions of opposite chiralities is predicted to appear along two separated oblique directions. In addition, valley filtering and beam splitting effects are easily tailored by dopant engineering techniques while the refraction of electron waves is dramatically modified by the tilt, thus paving the way for emerging applications in electron optics and valleytronics.Comment: 5 pages, 5 figures and Supplemental Material, submitted for publicatio

Stepped Graphene-based Aharonov-Bohm Interferometers

Aharonov-Bohm interferences in the quantum Hall regime are observed when electrons are transmitted between two edge channels. Such a phenomenon has been realized in 2D systems such as quantum point contacts, anti-dots and p-n junctions. Based on a theoretical investigation of the magnetotransport in stepped graphene, a new kind of Aharonov-Bohm interferometers is proposed herewith. Indeed, when a strong magnetic field is applied in a proper direction, oppositely propagating edge states can be achieved in both terrace and facet zones of the step, leading to the interedge scatterings and hence strong Aharonov-Bohm oscillations in the conductance in the quantum Hall regime. Taking place in the unipolar regime, this interference is also predicted in stepped systems of other 2D layered materials.Comment: 6 pages + 6 figures and a supplemental material, revised and resubmitte