Universal scaling limits of matrix models, and (p,q) Liouville gravity

We show that near a point where the equilibrium density of eigenvalues of a matrix model behaves like y ~ x^{p/q}, the correlation functions of a random matrix, are, to leading order in the appropriate scaling, given by determinants of the universal (p,q)-minimal models kernels. Those (p,q) kernels are written in terms of functions solutions of a linear equation of order q, with polynomial coefficients of degree at most p. For example, near a regular edge y ~ x^{1/2}, the (1,2) kernel is the Airy kernel and we recover the Airy law. Those kernels are associated to the (p,q) minimal model, i.e. the (p,q) reduction of the KP hierarchy solution of the string equation. Here we consider only the 1-matrix model, for which q=2.Comment: pdflatex, 44 pages, 2 figure

Focus in Ewe

International audience—In this paper, a strides detection algorithm is proposed using inertial sensors worn on the ankle. This innovative approach based on geometric patterns can detect both normal walking strides and atypical strides such as small steps, side steps and backward walking that existing methods struggle to detect. It is also robust in critical situations, when for example the wearer is sitting and moving the ankle, while most algorithms in the literature would wrongly detect strides

Determinantal formulae and loop equations

We prove that the correlations functions, generated by the determinantal process of the Christoffel-Darboux kernel of an arbitrary order 2 ODE, do satisfy loop equations.Comment: Latex, 35 pages few misprints correcte

Dynamic aspects of perception in binaural listening

Imperial Users onl

Pareto-efficiency and endogenous fertility: a simple model

This article is devoted to the study of the Pareto-efficiency of the competitive equilibrium for a simple overlapping generations economy with endogenous fertility. For CES utility and production functions, it is proved that the economic properties of the economy are closely related to the two elasticitiesof substitution. First, the competitive equilibrium exists and is unique if the sum of the two elasticities is not smaller than one. Secondly, a set of parameters is provided such that the equilibrium is both in under-accumulation and inefficient. Thirdly, a sufficient condition is proved that ensures that an equilibrium converging in under-accumulation is Pareto-efficient: the sum of the two elasticities must not be greater than two.endogenous fertility ; Pareto-efficiency

A notion of sufficient input

In this paper, we study a notion of sufficient input, i.e. input that allows to produce at least one unit of output when the other inputs are fixed at any positive level. We show that such an input allows to produce any positive amount of production. The main property of sufficient inputs is as follows. A input is sufficient if and only if the unit cost goes to zero when its price goes to zero.

Liberalization and Stock Market Co-Movement between Emerging Economies

In this paper, we investigate the impact of trade and financial liberalization on the degree of stock market co-movement among emerging economies. Using a sample of 25 developing countries observed over 15 years, we estimate the impact of reforms which aim at opening these countries to trade and financial channels to the rest of the world. The estimation of time-varying cross-country correlations allows the econometric investigation to be performed using a panel data framework, raising hence the quality of the statistical inference. Our results offer strong support in favor of a positive impact of trade and financial liberalization reforms on the degree of cross-country stock market linkages.stock market synchronization, financial integration, trade integration, emerging markets