On the approach to equilibrium for a polymer with adsorption and repulsion

We consider paths of a one-dimensional simple random walk conditioned to come back to the origin after L steps (L an even integer). In the 'pinning model' each path \eta has a weight \lambda^{N(\eta)}, where \lambda>0 and N(\eta) is the number of zeros in \eta. When the paths are constrained to be non-negative, the polymer is said to satisfy a hard-wall constraint. Such models are well known to undergo a localization/delocalization transition as the pinning strength \lambda is varied. In this paper we study a natural 'spin flip' dynamics for these models and derive several estimates on its spectral gap and mixing time. In particular, for the system with the wall we prove that relaxation to equilibrium is always at least as fast as in the free case (\lambda=1, no wall), where the gap and the mixing time are known to scale as L^{-2} and L^2\log L, respectively. This improves considerably over previously known results. For the system without the wall we show that the equilibrium phase transition has a clear dynamical manifestation: for \lambda \geq 1 the relaxation is again at least as fast as the diffusive free case, but in the strictly delocalized phase (\lambda < 1) the gap is shown to be O(L^{-5/2}), up to logarithmic corrections. As an application of our bounds, we prove stretched exponential relaxation of local functions in the localized regime.Comment: 43 pages, 5 figures; v2: corrected typos, added Table

On the probability of staying above a wall for the (2+1)-dimensional SOS model at low temperature

We obtain sharp asymptotics for the probability that the (2+1)-dimensional discrete SOS interface at low temperature is positive in a large region. For a square region $\Lambda$, both under the infinite volume measure and under the measure with zero boundary conditions around $\Lambda$, this probability turns out to behave like $\exp(-\tau_\beta(0) L \log L )$, with $\tau_\beta(0)$ the surface tension at zero tilt, also called step free energy, and $L$ the box side. This behavior is qualitatively different from the one found for continuous height massless gradient interface models.Comment: 21 pages, 6 figure

Examples of non-trivial contact mapping classes for overtwisted contact manifolds in all dimensions

We construct (infinitely many) examples in all dimensions of contactomorphisms of closed overtwisted contact manifolds that are smoothly isotopic but not contact-isotopic to the identity.Comment: v3: Considerable improvement in both content and form, thanks to referee's suggestions; version corresponding to the published one; 18 pages. v2: Minor changes with respect to the first version, 20 page

The Single Market and Synchronized Mechanisms for the Exercise of Administrative Functions: Converging Pathways or new Pathways for Integration? The Case of the European Banking Union

The EBU represents a clear investment in administrative integration with clear implications for the constitutional features of the EU. This paper aims to give an analysis of the administrative arrangements, through which the functions of supervision and resolution are affecting the single financial market. This case study is very interesting because these functions represent a genuine novelty in the history of financial integration since they are pre-ordained to a specific public interest: financial stability. Particularly, they cause a shift in the decision gradient from the technical to the political, as market integrity is less and less the key interest compared to financial stability. However, this wider discretionary power is not adequately counteracted by checks and balances in favour of accountability. As a result, the EBU makes a new contribution to the well-known ‘fragmentation of the executive power’ of the EU by introducing a new governance tool positioned between the Communitarian and Intergovernmental Method, but its development is still full of uncertainties given that constitutional equilibrium is far from being definitively reached

Effects of BBN on Population III stars

The presence (or absence) of CNO elements in the primordial gas determines different behaviours in population III stars formation and evolution: we therefore present an analysis of the main channels for the synthesis of these elements in BBN in order to understand, within a reliable interval, their abundance in the primordial material.Comment: 2 pages, Proceedings of the conference "Observing, Thinking and Mining the Universe" held in Sorrento (Italy), sept. 200