A renormalisation group approach to the universality of Wigner's semicircle law for random matrices with dependent entries

We show that if the non Gaussian part of the cumulants of a random matrix model obey some scaling bounds in the size of the matrix, then Wigner's semicircle law holds. This result is derived using the replica technique and an analogue of the renormalisation group equation for the replica effective action. This is a transcript of a talk given at "5th Winter Workshop on Non-Perturbative Quantum Field Theory" Sophia-Antipolis, March 2017 and is based on former work in collaboration with A. Tanasa and D.L. Vu, see arXiv:1609.01873 .Comment: 12 pages, 4 figures, to appear in the conference proceeding

Group field theories

Group field theories are particular quantum field theories defined on D copies of a group which reproduce spin foam amplitudes on a space-time of dimension D. In these lecture notes, we present the general construction of group field theories, merging ideas from tensor models and loop quantum gravity. This lecture is organized as follows. In the first section, we present basic aspects of quantum field theory and matrix models. The second section is devoted to general aspects of tensor models and group field theory and in the last section we examine properties of the group field formulation of BF theory and the EPRL model. We conclude with a few possible research topics, like the construction of a continuum limit based on the double scaling limit or the relation to loop quantum gravity through Schwinger-Dyson equationsComment: Lectures given at the "3rd Quantum Gravity and Quantum Geometry School", march 2011, Zakopan

Schwinger-Dyson Equations in Group Field Theories of Quantum Gravity

In this talk, we elaborate on the operation of graph contraction introduced by Gurau in his study of the Schwinger-Dyson equations. After a brief review of colored tensor models, we identify the Lie algebra appearing in the Schwinger-Dyson equations as a Lie algebra associated to a Hopf algebra of the Connes-Kreimer type. Then, we show how this operation also leads to an analogue of the Wilsonian flow for the effective action. Finally, we sketch how this formalism may be adapted to group field theories.Comment: talk given at "The XXIX International Colloquium on Group-Theoretical Methods in Physics", Chern Institute of Mathematics August 2012, submitted to the conference proceeding

Comparison of Nominal and Real Rigidities: Fiscal Policy Perspective

This paper examines the impact of nominal and real rigidities in the economy on the effects of fiscal policy. The study confirmed the hypothesis that both nominal and real rigidities enhance the impact of fiscal policy on the Polish economy. In the case of nominal price rigidity it was found that the impact of government spending on GDP depends on the conduct of monetary policy. On the other hand, under conditions of wage rigidity, the strength of fiscal multipliers depends on the slope of the labour supply curve. The study also examined two types of real rigidities - lack of access to the credit market, and consumer habits. Analyses show that the above rigidities result primarily in a strong positive relationship between government spending and the level of consumptionW pracy zbadano wpływ występowania sztywności nominalnych i realnych w gospodarce na charakter oddziaływania polityki fiskalnej. Potwierdzono hipotezę, że zarówno sztywności nominalne, jak i realne zwiększają siłę wpływu polityki fiskalnej na gospodarkę polską. W przypadku sztywności nominalnej cen uzyskano, że siła oddziaływania wydatków rządowych na PKB uzależniona jest od prowadzonej polityki pieniężnej. Natomiast w warunkach sztywności płac wysokość mnożników fiskalnych zależy od nachylenia krzywej podaży pracy. W pracy zbadano również dwa rodzaje sztywności realnych - brak dostępu do rynku kredytowego i występowanie przyzwyczajeń konsumpcyjnych. Z przeprowadzonych analiz wynika, że ww. sztywności skutkują przede wszystkim silną dodatnią zależnością pomiędzy wydatkami rządowymi a poziomem konsumpcji

Innovation Levels in the Economies of Central and Eastern Europe

The statistical data presented in this paper indicates that the innovative position of the CEECs is still unfavourable and relatively weak, with the exception of Slovenia and Estonia. Poland is in a particularly difficult situation, with many signs of stagnation with respect to innovation, keeping it at a low level (next to Bulgaria and Romania).Dane statystyczne przedstawione w artykule wskazują, że pozycja innowacyjna CEEC jest ciągle niekorzystna i relatywnie słaba, z wyjątkiem Słowenii i Estonii. W szczególnie trudnej sytuacji jest Polska, w której występuje najwięcej (obok Bułgarii i Rumunii) oznak stagnacji innowacyjnej na niskim poziomie

Estimating and Forecasting GDP in Poland with Dynamic Factor Model

Presented paper concerns the dynamic factor models theory and application in the econometric analysis of GDP in Poland. DFMs are used for construction of the economic indicators and in forecasting, in analyses of the monetary policy and international business cycles. In the article we compare the forecast accuracy of DFMs with the forecast accuracy of 2 competitive models: AR model and symptomatic model. We have used 41 quarterly time series from the Polish economy. The results are encouraging. The DFM outperforms other models. The best fitted to empirical data was model with 3 factors.Dynamic factor models, principal components analysis, GDP.

Legitimizing global economic governance through transnational parliamentarization: The parliamentary dimensions of the WTO and the World Bank

This paper discusses the potential contribution of parliamentary institutions and networks to the democratization of global economic governance. It places the analysis in the context of the larger debate on the democratic deficit of international economic institutions, in particular the WTO. On a theoretical level, the paper distinguishes different notions of legitimacy and democracy in order to identify which aspects of democratic legitimacy of global economic governance can be addressed through transnational parliamentarization. It is argued that national parliaments must react to the emergence of global economic governance in a multi-level system through new forms of transnational parliamentarization. In its empirical part, the paper assesses the Parliamentary Conference on the WTO (PCWTO) and the Parliamentary Network on the World Bank (PNoWB) as two examples of such transnational parliamentarization. Drawing on the theory of deliberative democracy the paper argues that the contribution of these settings to democratic global governance should not be measured on the basis of their formal decision-making power but with regard to their role as fora for transnational discourses and on their potential to empower national parliamentarians. -- Das Arbeitspapier untersucht den potentiellen Beitrag von parlamentarischen Institutionen und Netzwerken zur Demokratisierung des internationalen Wirtschaftssystems. Es stellt die Analyse in den Kontext der allgemeinen Debatte über das Demokratiedefizit der globalen Wirtschaftsinstitutionen, insbesondere der WTO. Auf theoretischer Ebene unterscheidet das Arbeitspapier verschiedene Konzeptionen von Legitimität und Demokratie, um herauszufiltern, welche Anforderungen demokratischer Legitimität durch Prozesse der transnationalen Parlamentarisierung erfüllt werden können. Das Arbeitspapier argumentiert, dass nationale Parlamente auf die Emergenz globaler Wirtschaftsinstitutionen im Mehrebenensystem durch neue Formen der transnationalen Parlamentarisierung reagieren müssen. In seinem empirischen Teil bewertet das Arbeitspapier die Parlamentarische Konferenz zur WTO (Parliamentary Conference on the WTO, PCWTO) und das Parlamentarische Netzwerk zur Weltbank (Parliamentary Network on the World Bank, PNoWB) als zwei Beispiele einer derartigen transnationalen Parlamentarisierung. Unter Rückgriff auf die Theorie der deliberativen Demokratie wird argumentiert, dass der Beitrag dieser Einrichtungen zu demokratischer gobal governance nicht anhand ihrer formalen Entscheidungsbefugnisse gemessen werden sollte, sondern mit Blick auf ihre Rolle als Foren für transnationale Diskurse und ihr Potential nationale Parlamentarier zu stärken.

Does a Progressive PIT Stabilize the Economy? A Comparison of Progressive and Flat Taxes

The aim of the article is to examine the impact of progressive personal income tax rates and the effectiveness of this tax as an automatic economic stabilizer. The assessment of automatic stabilizers is based on the estimates of tax cyclical components. The study shows that the output elasticity of PIT is higher than one, which means that the analysed tax acts relatively efficiently as an automatic stabilizer. However, it was also observed that the tax progressivity is not the main reason of the effectiveness of a progressive PIT as an automatic stabilizer. The study shows that changes in progressive rates of PIT, contrary to widespread opinions, have little effect on the effectiveness of passive fiscal policy. Personal income tax acts as automatic stabilizer mostly due not to the progressive tax rates, but because of the sensitivity of employment to GDP fluctuations

Polchinski's exact renormalisation group for tensorial theories: Gaussian universality and power counting

In this paper, we use the exact renormalisation in the context of tensor models and tensorial group field theories. As a byproduct, we rederive Gaussian universality for random tensors and provide a general power counting for Abelian tensorial field theories with a closure constraint, leading us to a only five renormalizable theories.Comment: 22 pages, 4 figure

Analyticity results for the cumulants in a random matrix model

The generating function of the cumulants in random matrix models, as well as the cumulants themselves, can be expanded as asymptotic (divergent) series indexed by maps. While at fixed genus the sums over maps converge, the sums over genera do not. In this paper we obtain alternative expansions both for the generating function and for the cumulants that cure this problem. We provide explicit and convergent expansions for the cumulants, for the remainders of their perturbative expansion (in the size of the maps) and for the remainders of their topological expansion (in the genus of the maps). We show that any cumulant is an analytic function inside a cardioid domain in the complex plane and we prove that any cumulant is Borel summable at the origin