The Riemann-Hilbert approach to obtain critical asymptotics for Hamiltonian perturbations of hyperbolic and elliptic systems

The present paper gives an overview of the recent developments in the description of critical behavior for Hamiltonian perturbations of hyperbolic and elliptic systems of partial differential equations. It was conjectured that this behavior can be described in terms of distinguished Painlev\'e transcendents, which are universal in the sense that they are, to some extent, independent of the equation and the initial data. We will consider several examples of well-known integrable equations that are expected to show this type of Painlev\'e behavior near critical points. The Riemann-Hilbert method is a useful tool to obtain rigorous results for such equations. We will explain the main lines of this method and we will discuss the universality conjecture from a Riemann-Hilbert point of view.Comment: review paper, 22 pages, 4 figure

Overview on a selection of recent works in asymptotic analysis for wave propagation problems

We give a brief survey of some recent advances of asymptotic analysis methods applied to wave propagation problem

Essential spectrum of local multi-trace boundary integral operators

Considering pure transmission scattering problems in piecewise constant media, we derive an exact analytic formula for the spectrum of the corresponding local multi-trace boundary integral operators in the case where the geometrical configuration does not involve any junction point and all wave numbers equal. We deduce from this the essential spectrum in the case where wave numbers vary. Numerical evidences of these theoretical results are also presented

Numerical study of the small dispersion limit of the Korteweg-de Vries equation and asymptotic solutions

We study numerically the small dispersion limit for the Korteweg-de Vries (KdV) equation $u_t+6uu_x+\epsilon^{2}u_{xxx}=0$ for $\epsilon\ll1$ and give a quantitative comparison of the numerical solution with various asymptotic formulae for small $\epsilon$ in the whole $(x,t)$-plane. The matching of the asymptotic solutions is studied numerically

Estimating the effects of fiscal policy under the budget constraint

I reconsider the short-term effects of fiscal policy when both government spending and taxes are allowed to respond to the level of public debt. I embed the long-term government budget constraint in a VAR, and apply this common trends model to US quarterly data. The main finding is that fiscal consolidation has expansionary effects on output and inflation. Non-Keynesian effects also dominate when debt expands. The expectation of policy adjustments to guarantee fiscal sustainability by future tax rises or spending cuts contracts output today.Fiscal policy, sustainability, spending, taxes, common trends, SVAR

If you want me to stay, pay

Devolution of political power is constantly on the political agenda in both Italy and Spain. Fiscal policy in these countries has granted specific privileges to some regions. Valle d’Aosta/Vallée d’Aoste (VdA) and País Vasco/Euskadi (PV) have an extensive say over spending decisions, and receive nearly all regional tax revenues. Although both VdA and PV are among the richest regions in each country, both are net beneficiaries of the fiscal equalisation system. This preferential treatment is the outcome of a fiscal system with limits on taxing power and debt issuance, and is meant as a compensation for the lack of autonomy. It so prevents calls for more fiscal autonomy, or even outright secession. The economic effects of this asymmetric federalism are negative. Although partial equalisation reduces excessive redistribution built in the fiscal equalisation system, more autonomy could pay off with more efficient government. Asymmetric federalism moreover creates a political impasse in the negotiation of a more efficient tax system and financing arrangement.fiscal federalism, equalisation, secession, Valle d’Aosta, País Vasco. JEL classification:H70, H73, H77

Policy Mix and Debt Sustainability: Evidence from Fiscal Policy Rules

This paper characterises rules-based fiscal policy setting. Basically, we translate a standard monetary policy rule into a simple fiscal policy rule. We then infer on fiscal policymakers' reaction coefficients by testing the rule with GMM. Interaction is also tested directly by the inclusion of monetary policy setting. Our results qualify existing evidence on systematic fiscal policy in two respects. First, fiscal policy usually stabilises public debt. And there is indeed substantial interaction between fiscal and monetary policy via the debt channel. Second, sustainability is achieved with a “stop-go” cycle of consolidation. Consolidation does not come at the cost of less cyclical stabilisation unless debt ratios are high.monetary policy, fiscal policy, policy interaction and policy rules, debt sustainability

Random matrices with equispaced external source

We study Hermitian random matrix models with an external source matrix which has equispaced eigenvalues, and with an external field such that the limiting mean density of eigenvalues is supported on a single interval as the dimension tends to infinity. We obtain strong asymptotics for the multiple orthogonal polynomials associated to these models, and as a consequence for the average characteristic polynomials. One feature of the multiple orthogonal polynomials analyzed in this paper is that the number of orthogonality weights of the polynomials grows with the degree. Nevertheless we are able to characterize them in terms of a pair of 2 x 1 vector-valued Riemann-Hilbert problems, and to perform an asymptotic analysis of the Riemann-Hilbert problems.Comment: 53 pages, 9 figures; textual changes and minor typos correcte