Exponential or power law? How to select a stable distribution of probability in a physical system

A mapping of nonextensive statistical mechanics into Gibbs' statistical mechanics exists, which leads to a generalization of Einstein's formula for fluctuations. A unified treatment of stability of relaxed states in nonextensive statistical mechanics and Gibbs' statistical mechanics follows. The former and the latter are endowed with probability distribution of microstates ruled by power laws and Boltzmann exponentials respectively. We apply our treatment to the relaxed states described by a 1D nonlinear FokkerPlanck equation. If the latter is associated to the stochastic differential equation obtained in the continuous limit from a 1D, autonomous, discrete map affected by noise, then we may ascertain whether if a relaxed state follow a power law distribution (and with which exponent) by looking at both map dynamics and noise level, with no assumptions concerning the additive or multiplicative nature of the noise and with no numerical computation of the orbits. Results agree with the simulations of Sanchez et al. EPJ 143.1 (2007) 141-143 concerning relaxation to a Pareto-like distribution.Comment: Conference paper, 3 figure

Legal Families and Environmental Protection: Is there a Causal Relationship?

In this paper we build up the analysis of La Porta et al. (1998), to investigate the importance of legal families in explaining the variations in pollution emissions in different countries. The main intuition behind our analysis is that the nations in which the rights of shareholders are more protected, promote real and financial investment; this increases the speed at which the per-capita income corresponding to the declining branch of the Environmental Kutznets Curve (EKC) is achieved. In econometrics different regression analyses were performed using as dependent variables three different kinds of pollutants (CO2, fine suspended particulates and waste), including as an explanation some financial variables never before considered in this kind of study.Dummy Variables, Environmental Kutznets Curve, Legal Families, Panel Data, Pollution Emissions

Natural Resources Dynamics: Another Look

In this paper we study the problem of exhaustible resources and renewable resources in a theoretical endogenous growth framework, under various assumptions. In particular, we consider the hypotheses that those two inputs are or are not technologically perfect substitutes of each other. Moreover, we develop the starting model accounting for the negative externality of waste accumulation. Finally, a comparative analysis is made between Pigouvian tax and waste recycling as an environmental policy to internalize the negative externality represented by refuse accumulation.Economic growth, Endogenous technological progress, Exhaustible resources, Pigouvian taxes, Renewable natural inputs, Technological substitutability

Is the Discount Rate Relevant in Explaining the Environmental Kuznets Curve?

In this paper we use Pindyck’s model (2002) to show that the discount rate may play an important role in explaining for the income-pollution pattern observed in the real world. Low levels of income involve high values of discount rate, that are obstacles to the adoption of a pollution abatement policy. Only when the discount rate falls, as a consequence of growth, will it be possible to implement measures for emissions reduction. Thus we are able to derive an inverse U-shaped income-pollution pattern, making use of an argument that has never yet been introduced in the economic debate on this issue.Discount rate, Environmental Kuznets Curve, Income, Stock pollutants

Two-loop master integrals for the leading QCD corrections to the Higgs coupling to a WW pair and to the triple gauge couplings ZWWZWW and γ∗WW\gamma^*WW

We compute the two-loop master integrals required for the leading QCD corrections to the interaction vertex of a massive neutral boson $X^0$, e.g. $H,Z$ or $\gamma^{*}$, with a pair of $W$ bosons, mediated by a $SU(2)_L$ quark doublet composed of one massive and one massless flavor. All the external legs are allowed to have arbitrary invariant masses. The Magnus exponential is employed to identify a set of master integrals that, around $d=4$ space-time dimensions, obey a canonical system of differential equations. The canonical master integrals are given as a Taylor series in $\epsilon = (4-d)/2$, up to order four, with coefficients written as combination of Goncharov polylogarithms, respectively up to weight four. In the context of the Standard Model, our results are relevant for the mixed EW-QCD corrections to the Higgs decay to a $W$ pair, as well as to the production channels obtained by crossing, and to the triple gauge boson vertices $ZWW$ and $\gamma^*WW$.Comment: 42 pages, 5 figures, 2 ancillary file

Three-loop master integrals for ladder-box diagrams with one massive leg

The three-loop master integrals for ladder-box diagrams with one massive leg are computed from an eighty-five by eighty-five system of differential equations, solved by means of Magnus exponential. The results of the considered box-type integrals, as well as of the tower of vertex- and bubble-type master integrals associated to subtopologies, are given as a Taylor series expansion in the dimensional regulator parameter epsilon = (4-d)/2. The coefficients of the series are expressed in terms of uniform weight combinations of multiple polylogarithms and transcendental constants up to weight six. The considered integrals enter the next-to-next-to-next-to-leading order virtual corrections to scattering processes like the three-jet production mediated by vector boson decay, V* -> jjj, as well as the Higgs plus one-jet production in gluon fusion, pp -> Hj.Comment: 44 pages, 5 figures, 2 ancillary file