We compute correlation functions of inverse powers and ratios of characteristic polynomials for random matrix models with complex eigenvalues. Compact expressions are given in terms of orthogonal polynomials in the complex plane as well as their Cauchy transforms, generalizing previous expressions for real eigenvalues. We restrict ourselves to ratios of characteristic polynomials over their complex conjugate.
The relationship between income of households and their carbon emissions is often summed up by a number, the elasticity of the carbon footprint with respect to income. I survey here the cross-sectional studies of household carbon footprints and their estimation of elasticities with respect to income and with respect to expenditures. The distinction between the two elasticities comes from the fact that the saving rate rises with income.I compile published estimates of elasticities of carbon footprint or energy requirements, and I compute new estimates. This totals around eighty estimates (a third of which are newly computed) for over twenty countries. It shows that, generally, the carbon footprint grows less rapidly than expenditures, and confirms that the incomeelasticity is lower than expenditure-elasticity. Unambiguously, the assumption of an income-elasticity equal to 1 is not supported by the published literature.I discuss the difference between carbon inequality and carbon concentration, the ambiguity in the literature between income-elasticity and expenditures-elasticity. I present the limitations of our knowledge on the income-carbon footprint relationship, from contestable assumption in the methodology as well as measurement errors in household budget surveys. I examine how elasticity can be used in "top-down" assessment of global distribution of carbon footprint.
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