Reconstructing WKB from topological recursion

We prove that the topological recursion reconstructs the WKB expansion of a quantum curve for all spectral curves whose Newton polygons have no interior point (and that are smooth as affine curves). This includes nearly all previously known cases in the literature, and many more; in particular, it includes many quantum curves of order greater than two. We also explore the connection between the choice of ordering in the quantization of the spectral curve and the choice of integration divisor to reconstruct the WKB expansion.Comment: 68 pages, 9 figures. v2: published version (improved presentation

Think globally, compute locally

We introduce a new formulation of the so-called topological recursion, that is defined globally on a compact Riemann surface. We prove that it is equivalent to the generalized recursion for spectral curves with arbitrary ramification. Using this global formulation, we also prove that the correlation functions constructed from the recursion for curves with arbitrary ramification can be obtained as suitable limits of correlation functions for curves with only simple ramification. It then follows that they both satisfy the properties that were originally proved only for curves with simple ramification.Comment: 37 pages, v2: published versio

Evidences of Interdependence and Contagion using a Frequency Domain Framework

The purpose of this paper is to propose a new measure of contagion. Our approach to testing contagion is based on the frequency analysis of causality developed recently by Breitung and Candelon (2004). This approach handles, in a unified framework, several of the statistical problems identified in the literature. It also permits clear differentiation between temporary and permanent shifts in cross-market linkages: the first case is contagion while the second one is simply a measure of interdependence among markets. In examining the ”Tequila” and Asian crises, we find evidence for contagion during both. It also turns out that during the Asian crisis both contagion and higher interdependence have contributed simultaneously to the diffusion of the crisis in Asia. The spillover effects of these crises have been geographically limited to the region where the shock originated.macroeconomics ;

Critical Gaussian multiplicative chaos: Convergence of the derivative martingale

In this paper, we study Gaussian multiplicative chaos in the critical case. We show that the so-called derivative martingale, introduced in the context of branching Brownian motions and branching random walks, converges almost surely (in all dimensions) to a random measure with full support. We also show that the limiting measure has no atom. In connection with the derivative martingale, we write explicit conjectures about the glassy phase of log-correlated Gaussian potentials and the relation with the asymptotic expansion of the maximum of log-correlated Gaussian random variables.Comment: Published in at http://dx.doi.org/10.1214/13-AOP890 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Log-correlated Gaussian fields: an overview

We survey the properties of the log-correlated Gaussian field (LGF), which is a centered Gaussian random distribution (generalized function) $h$ on $\mathbb R^d$, defined up to a global additive constant. Its law is determined by the covariance formula $$\mathrm{Cov}\bigl[ (h, \phi_1), (h, \phi_2) \bigr] = \int_{\mathbb R^d \times \mathbb R^d} -\log|y-z| \phi_1(y) \phi_2(z)dydz$$ which holds for mean-zero test functions $\phi_1, \phi_2$. The LGF belongs to the larger family of fractional Gaussian fields obtained by applying fractional powers of the Laplacian to a white noise $W$ on $\mathbb R^d$. It takes the form $h = (-\Delta)^{-d/4} W$. By comparison, the Gaussian free field (GFF) takes the form $(-\Delta)^{-1/2} W$ in any dimension. The LGFs with $d \in \{2,1\}$ coincide with the 2D GFF and its restriction to a line. These objects arise in the study of conformal field theory and SLE, random surfaces, random matrices, Liouville quantum gravity, and (when $d=1$) finance. Higher dimensional LGFs appear in models of turbulence and early-universe cosmology. LGFs are closely related to cascade models and Gaussian branching random walks. We review LGF approximation schemes, restriction properties, Markov properties, conformal symmetries, and multiplicative chaos applications.Comment: 24 pages, 2 figure

A non-conservative Harris ergodic theorem

We consider non-conservative positive semigroups and obtain necessary and sufficient conditions for uniform exponential contraction in weighted total variation norm. This ensures the existence of Perron eigenelements and provides quantitative estimates of the spectral gap, complementing Krein-Rutman theorems and generalizing probabilistic approaches. The proof is based on a non-homogenous $h$-transform of the semigroup and the construction of Lyapunov functions for this latter. It exploits then the classical necessary and sufficient conditions of Harris's theorem for conservative semigroups and recent techniques developed for the study of absorbed Markov processes. We apply these results to population dynamics. We obtain exponential convergence of birth and death processes conditioned on survival to their quasi-stationary distribution, as well as estimates on exponential relaxation to stationary profiles in growth-fragmentation PDEs

Real Exchange Rates, Commodity Prices and Structural Factors in Developing Countries

This paper provides new empirical evidence about the relationship that may exist between real exchange rates and commodity prices in developing countries that are specialized in the export of a main primary commodity. It investigates how structural factors like the exchange rate regime, the degree of financial and trade openness, the degree of export concentration and the type of the commodity exports affect the strength of the commodity price-real exchange rate dependence.Real exchange rates, commodity prices, exchange rate regime, financial openness, panel analysis

Real exchanges rates in commodity producing countries : A reappraisal

Commodity currency literature recently stressed the importance of commodity prices as a determinant of real exchange rates in developing countries (Cashin, Cespedes and Sahay 2004). We provide new empirical evidence on this issue by focusing on countries which are specialized in the ex-port of one leading commodity. For those countries, we investigate to which extent their real exchange rate is sensitive to price fluctuations of their dominant commodity. By using non-stationary panel techniques robust to cross-sectional-dependence, we find that the price of the dominant commodity has a significant long-run impact on the real exchange rate when the exports of the leading commodity have a share of at least 20 percent in the country’s total exports of merchandises. Our results also show that the larger the share, the larger the size of the impact.real exchange rates, commodity prices, non-stationary panel