Stein's method, Malliavin calculus, Dirichlet forms and the fourth moment theorem

The fourth moment theorem provides error bounds of the order $\sqrt{{\mathbb E}(F^4) - 3}$ in the central limit theorem for elements $F$ of Wiener chaos of any order such that ${\mathbb E}(F^2) = 1$. It was proved by Nourdin and Peccati (2009) using Stein's method and the Malliavin calculus. It was also proved by Azmoodeh, Campese and Poly (2014) using Stein's method and Dirichlet forms. This paper is an exposition on the connections between Stein's method and the Malliavin calculus and between Stein's method and Dirichlet forms, and on how these connections are exploited in proving the fourth moment theorem

Diffractive Dijet Production in Deep Inelastic Scattering and Photon-Hadron Collisions in the Color Glass Condensate

We study exclusive dijet production in coherent diffractive processes in deep inelastic scattering and real (and virtual) photon-hadron ($\gamma^{(*)}$-h) collisions in the Color Glass Condensate formalism at leading order. We show that the diffractive dijet cross section is sensitive to the color-dipole orientation in the transverse plane, and is a good probe of possible correlations between the $q\bar{q}$-dipole transverse separation vector \r and the dipole impact parameter \b. We also investigate the diffractive dijet azimuthal angle correlations and $t$-distributions in $\gamma^{(*)}$-h collisions and show that they are sensitive to gluon saturation effects in the small-$x$ region. In particular, we show that the $t$-distribution of diffractive dijet photo-production off a proton target exhibits a dip-type structure in the saturation region. This effect is similar to diffractive vector meson production. Besides, at variance with the inclusive case, the effect of saturation leads to stronger azimuthal correlations between the jets.Comment: 15 pages, 10 figures; v2: a clarifying Appendix added, 3 new plots added, references added. The version to appear in PL

On the use of the IAST method for gas separation studies in porous materials with gate-opening behavior

Highly flexible nanoporous materials, exhibiting for instance gate opening or breathing behavior, are often presented as candidates for separation processes due to their supposed high adsorption selectivity. But this view, based on "classical" considerations of rigid materials and the use of the Ideal Adsorbed Solution Theory (IAST), does not necessarily hold in the presence of framework deformations. Here, we revisit some results from the published literature and show how proper inclusion of framework flexibility in the osmotic thermodynamic ensemble drastically changes the conclusions, in contrast to what intuition and standard IAST would yield. In all cases, the IAST method does not reproduce the gate-opening behavior in the adsorption of mixtures, and may overestimates the selectivity by up to two orders of magnitude

Pork Versus Public Goods: An Experimental Study of Public Good Provision Within a Legislative Bargaining Framework

We experimentally investigate a legislative bargaining model with both public and particularistic goods. Consistent with the qualitative implications of the model: There is near exclusive public good provision in the pure public good region, in the pure private good region minimum winning coalitions sharing private goods predominate, and in the ‘mixed’ region proposers generally take some particularistic goods for themselves, allocating the remainder to public goods. As in past experiments, proposer ower is not nearly as strong as predicted, resulting in public good provision decreasing in the mixed region as its relative value increases, which is inconsistent with the theory.Legislative Bargaining, Public Goods, Efficiency

On tidal capture of primordial black holes by neutron stars

The fraction of primordial black holes (PBHs) of masses $10^{17} - 10^{26}$ g in the total amount of dark matter may be constrained by considering their capture by neutron stars (NSs), which leads to the rapid destruction of the latter. The constraints depend crucially on the capture rate which, in turn, is determined by the energy loss by a PBH passing through a NS. Two alternative approaches to estimate the energy loss have been used in the literature: the one based on the dynamical friction mechanism, and another on tidal deformations of the NS by the PBH. The second mechanism was claimed to be more efficient by several orders of magnitude due to the excitation of particular oscillation modes reminiscent of the surface waves. We address this disagreement by considering a simple analytically solvable model that consists of a flat incompressible fluid in an external gravitational field. In this model, we calculate the energy loss by a PBH traversing the fluid surface. We find that the excitation of modes with the propagation velocity smaller than that of PBH is suppressed, which implies that in a realistic situation of a supersonic PBH the large contributions from the surface waves are absent and the above two approaches lead to consistent expressions for the energy loss.Comment: 7 page

Slow quench dynamics of Mott-insulating regions in a trapped Bose gas

We investigate the dynamics of Mott-insulating regions of a trapped bosonic gas as the interaction strength is changed linearly with time. The bosonic gas considered is loaded into an optical lattice and confined to a parabolic trapping potential. Two situations are addressed: the formation of Mott domains in a superfluid gas as the interaction is increased, and their melting as the interaction strength is lowered. In the first case, depending on the local filling, Mott-insulating barriers can develop and hinder the density and energy transport throughout the system. In the second case, the density and local energy adjust rapidly whereas long range correlations require longer time to settle. For both cases, we consider the time evolution of various observables: the local density and energy, and their respective currents, the local compressibility, the local excess energy, the heat and single particle correlators. The evolution of these observables is obtained using the time-dependent density-matrix renormalization group technique and comparisons with time-evolutions done within the Gutzwiller approximation are provided.Comment: 15 pages, 13 figure