Effective inverse spectral problem for rational Lax matrices and applications

We reconstruct a rational Lax matrix of size R+1 from its spectral curve (the desingularization of the characteristic polynomial) and some additional data. Using a twisted Cauchy--like kernel (a bi-differential of bi-weight (1-nu,nu)) we provide a residue-formula for the entries of the Lax matrix in terms of bases of dual differentials of weights nu and 1-nu respectively. All objects are described in the most explicit terms using Theta functions. Via a sequence of ``elementary twists'', we construct sequences of Lax matrices sharing the same spectral curve and polar structure and related by conjugations by rational matrices. Particular choices of elementary twists lead to construction of sequences of Lax matrices related to finite--band recurrence relations (i.e. difference operators) sharing the same shape. Recurrences of this kind are satisfied by several types of orthogonal and biorthogonal polynomials. The relevance of formulae obtained to the study of the large degree asymptotics for these polynomials is indicated.Comment: 33 pages. Version 2 with added references suggested by the refere

Free Energy of the Two-Matrix Model/dToda Tau-Function

We provide an integral formula for the free energy of the two-matrix model with polynomial potentials of arbitrary degree (or formal power series). This is known to coincide with the tau-function of the dispersionless two--dimensional Toda hierarchy. The formula generalizes the case studied by Kostov, Krichever, Mineev-Weinstein, Wiegmann, Zabrodin and separately Takhtajan in the case of conformal maps of Jordan curves. Finally we generalize the formula found in genus zero to the case of spectral curves of arbitrary genus with certain fixed data.Comment: Ver 2: 18 pages added important formulas for higher genus spectral curves, few typos removed (and few added). Ver 3: 19 pages (minor changes). Typos removed, added appendix and improved exposition Ver 4: 19 pages, minor corrections. Version submitted Ver 4; corrections prompted by referee and accepted in Nuclear Phys.

Cauchy Biorthogonal Polynomials

The paper investigates the properties of certain biorthogonal polynomials appearing in a specific simultaneous Hermite-Pade' approximation scheme. Associated to any totally positive kernel and a pair of positive measures on the positive axis we define biorthogonal polynomials and prove that their zeroes are simple and positive. We then specialize the kernel to the Cauchy kernel 1/{x+y} and show that the ensuing biorthogonal polynomials solve a four-term recurrence relation, have relevant Christoffel-Darboux generalized formulae, and their zeroes are interlaced. In addition, these polynomial solve a combination of Hermite-Pade' approximation problems to a Nikishin system of order 2. The motivation arises from two distant areas; on one side, in the study of the inverse spectral problem for the peakon solution of the Degasperis-Procesi equation; on the other side, from a random matrix model involving two positive definite random Hermitian matrices. Finally, we show how to characterize these polynomials in term of a Riemann-Hilbert problem.Comment: 38 pages, partially replaces arXiv:0711.408

Decomposing Quantum Fields on Branes

We provide a method to decompose the two-point function of a quantum field on a warped manifold in terms of fields living on a lower-dimensional manifold. We discuss explicit applications to Minkowski, de Sitter and anti-de Sitter quantum field theories. This decomposition presents a remarkable analogy with the holography principle, in the sense that physics in d+1 dimensions may be encoded into the physics in one dimension less. Moreover in a context a la Randall--Sundrum, the method outlined here allows a mechanism of generation of mass-spectra in the 3-brane (or more generally a d-1-brane).Comment: 25 page

Finance and welfare states in globalizing markets

It is theoretically clear and may be verified empirically that efficient financial markets can make it less necessary for policy to try and offset the welfare effects of labour income risk and unequal consumption dynamics. The literature has also pointed out that, since international competition exposes workers to new sources of risk at the same time as it makes it easier for individual choices to undermine collective policies, international economic integration makes insurance-oriented government policies more beneficial as well as more difficult to implement. This paper reviews the economic mechanisms underlying these insights and assesses their empirical relevance in cross-country panel data sets. Interactions between indicators of international economic integration, of government economic involvement, and of financial development are consistent with the idea that financial market development can substitute public schemes when economic integration calls for more effective household consumption smoothing. The paper’s theoretical perspective and empirical evidence suggest that to the extent that governments can foster financial market development by appropriate regulation and supervision, they should do so more urgently at times of intense and increasing internationalization of economic relationships. JEL Classification: G1, E2

A Social Union for the EU? Pro: An EU-Level Social Policy

Sozialpolitik, Europäische Integration, Sozialstaat, Europäische Wirtschafts- und Währungsunion, Social policy, European integration, Welfare state, European Economic and Monetary Union

Labour Markets in EMU - What has changed and what needs to change

This paper reviews theoretical and empirical aspects of the interaction between Europe's Economic and Monetary Union and recent labour market developments. Policies meant to increase and stabilize labour incomes also tend to reduce employment and productivity, theory suggests that the latter effects should be sharper and more relevant within an integrated market area, making it harder for National policy makers to address the consequences of financial and other market imperfections. Empirical patterns of policy and outcome indicators in member and non-member countries of EMU are consistent with that theoretical mechanism. In the data, tighter economic integration is associated with better employment performance, substantial deregulation, sharper disemployment effects of remaining regulatory differences, and somewhat higher inequality and larger private financial market volume..labour market, monetary union, unemployment, employment, labour income, Bertola