Alien Calculus and non perturbative effects in Quantum Field Theory

In many domains of physics, methods are needed to deal with non-perturbative aspects. I want here to argue that a good approach is to work on the Borel transforms of the quantities of interest, the singularities of which give non-perturbative contributions. These singularities in many cases can be largely determined by using the alien calculus developed by Jean \'Ecalle. My main example will be the two point function of a massless theory given as a solution of a renormalization group equation.Comment: 4 pages, double-colum

On the icosahedron: from two to three dimensions

In his famous book, Felix Klein describes a complex variable for the quotients of the ordinary sphere by the finite groups of rotations and in particular for the most complex situation of the quotient by the symmetry group of the icosahedron. The purpose of this work and its sequels is to obtain similar results for the quotients of the three--dimensional sphere. Various properties of the group $SU(2)$ and of its representations are used to obtain explicit expressions for coordinates and the relations they satisfy.Comment: 8 page

Consistency of Bayes estimators of a binary regression function

When do nonparametric Bayesian procedures ``overfit''? To shed light on this question, we consider a binary regression problem in detail and establish frequentist consistency for a certain class of Bayes procedures based on hierarchical priors, called uniform mixture priors. These are defined as follows: let $\nu$ be any probability distribution on the nonnegative integers. To sample a function $f$ from the prior $\pi^{\nu}$, first sample $m$ from $\nu$ and then sample $f$ uniformly from the set of step functions from $[0,1]$ into $[0,1]$ that have exactly $m$ jumps (i.e., sample all $m$ jump locations and $m+1$ function values independently and uniformly). The main result states that if a data-stream is generated according to any fixed, measurable binary-regression function $f_0\not\equiv1/2$, then frequentist consistency obtains: that is, for any $\nu$ with infinite support, the posterior of $\pi^{\nu}$ concentrates on any $L^1$ neighborhood of $f_0$. Solution of an associated large-deviations problem is central to the consistency proof.Comment: Published at http://dx.doi.org/10.1214/009053606000000236 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Higher Order Corrections to the Asymptotic Perturbative Solution of a Schwinger-Dyson Equation

Building on our previous works on perturbative solutions to a Schwinger-Dyson for the massless Wess-Zumino model, we show how to compute 1/n corrections to its asymptotic behavior. The coefficients are analytically determined through a sum on all the poles of the Mellin transform of the one loop diagram. We present results up to the fourth order in 1/n as well as a comparison with numerical results. Unexpected cancellations of zetas are observed in the solution, so that no even zetas appear and the weight of the coefficients is lower than expected, which suggests the existence of more structure in the theory.Comment: 16 pages, 2 figures. Some points clarified, typos corrected, matches the version to be published in Lett. Math. Phy

Prices, Wages and Fertility in Pre-Industrial England

A two-sector Malthusian model is formulated in terms of a cointegrated vector autoregressive (CVAR) model on error correction form. The model allows for both agricultural product wages and relative prices to affect fertility. The model is estimated using new data for the pre-industrial period in England, and the analysis reveals a strong, positive effect of agricultural wages as well as a small and, surprisingly, positive effect of real agricultural prices on fertility. Furthermore, it is demonstrated that there is constant returns to scale with respect to labour in the manufacturing sector and strongly decreasing returns to scale in the agricultural sector.Malthus; cointegration; pre-industrial England

Sticky prices and monetary policy : evidence from disaggregated U.S. data

This paper uses factor-augmented vector autoregressions (FAVAR) estimated using a large data set to disentangle fluctuations in disaggregated consumer and producer prices which are due to macroeconomic factors from those due to sectorial conditions. This allows us to provide consistent estimates of the effects of US monetary policy on disaggregated prices. While sectorial prices respond quickly to sector-specific shocks, we find that for a large number of price series, there is a significant delay in the response of prices to monetary policy shocks. In addition, price responses display little evidence of a “price puzzle,” contrary to existing studies based on traditional VARs. The observed dispersion in the reaction of producer prices is relatively well explained by the degree of market power, as predicted by models with monopolistic competition. JEL Classification: E32, E5

(WP 2010-07) Examining Megachurch Growth: Free Riding, Fit, and Faith

Megachurches are thriving in religious markets at a time when Americans are asserting their ability as consumers of religious products to engage in religious switching. The apparent success of megachurches, which often provide a low cost and low commitment path by which religious refugees may join the church, seems to challenge Iannocconne’s theory that high commitment churches will thrive while low commitment churches will atrophy. This paper employs a signaling model to illustrate the strategy and organizational forms megachurches employ to indicate a match between what the church produces and the religious refugee wishes to consume in an effort to increase their membership. The model illustrates that megachurches expect little in regard to financial or time commitment of new attendees. However, once the attendees perceive a good fit with the church, the megachurch increases its expectation of commitment. Data from the FACT2000 survey provide evidence in support of the model’s predictions