Study of θ\theta dependence in Yang-Mills theories on the lattice

We discuss the use of field theoretical techniques in the lattice determination of the free energy dependence on the $\theta$ angle in SU(N) Yang-Mills theories.Comment: 5 pages. Talk at the International Workshop on QCD: QCD@Work 2003 - Conversano (Italy) 14-18 June 2003 (eConf C030614

Field theoretical approach to the study of theta dependence in Yang-Mills theories on the lattice

We discuss the extension of the field theoretical approach, already used in the lattice determination of the topological susceptibility, to the computation of further terms in the expansion of the ground state energy $F(\theta)$ around $\theta = 0$ in SU(N) Yang-Mills theories. In particular we determine the fourth order term in the expansion for SU(3) pure gauge theory and compare our results with previous cooling determinations. In the last part of the paper we make some considerations about the nature of the ultraviolet fluctuations responsible for the renormalization of the lattice topological charge correlation functions; in particular we propose and test an ansatz which leads to improved estimates of the fourth and higher order terms in the expansion of F(\theta).Comment: 20 page

Lattice QCD with purely imaginary sources at zero and non-zero temperature

We discuss various aspects and recent progress concerning lattice QCD studies in the presence of external sources. We focus, in particular, on issues regarding QCD with non-zero imaginary chemical potentials or with a $\theta$-term, and on the properties of strongly interacting matter in the presence of electromagnetic background fields.Comment: 15 pages, 2 figures, plenary talk at the 32nd International Symposium on Lattice Field Theory (23-28 June 2014, Columbia University, New York, NY, USA). Minor changes, references adde

High-Temperature QCD: theory overview

We review the recent progress achieved in the theoretical investigation of Quantum Chromodynamics in the high temperature regime, with a focus on results achieved by lattice QCD simulations. The discussion covers the structure of the phase diagram and the properties of the strongly interacting medium at finite T and small baryon chemical potential.Comment: 7 pages, 2 figures, Proceedings of the Quark Matter 2018 conference, Venice, Ital

Actual and perceived inflation

The concept of inflation perceived by consumers came in the recent debate on inflation since it may affect consumer behaviour even if the perception was completely wrong. A misperception of inflation occurs particularly when households tend to label incorrectly inflation what really is a reduction in their disposable income, as in declining or stagnant economies and during public budget consolidation processes. Also a cash changeover may alter the perception of price changes. Nevertheless, even in a perfect perception framework, each consumer evaluates the inflation rate taking into account only his own consumption basket and the dynamics of the particular prices he pays. Hence, perceived inflation may differ systematically from the official one calculated by the statistical agencies, that necessarily make use of a common basket of consumption and the average market price of each product. The official inflation rate may be either beyond or below the average individual inflation rate in accordance with the sign of the covariance between individual budget shares and the corresponding price changes. Since economic theory suggests that the latter sign is positive under price discrimination, inflation faced by consumers is often higher than the official one. As far as the perceived inflation is strictly related to the cost of living, an aggregation fallacy may bias downward the estimation of official consumer price indices. At variance, just under price discrimination, firms tend to perceive an inflation rate very close to the official one, or even smaller. The arguments above provide a number of testable consequences.Aggregation fallacy; Inflation measurement; Perceived inflation; Price discrimination

Hedonic Regressions, Matched Models and Economic Theory

Quality adjustment of price indexes affects the analysis of many sensitive economic issues, such as real growth, productivity, international competitiveness, real wages, per-capita consumption and poverty, other than inflation. Hedonic methods are often recommended and increasingly used in the compilation of consumer price indexes. Nevertheless many official statistical agencies continue adopting traditional methods considering only the dynamics of prices of products matching in two adjacent periods of time. Indeed, a number of studies have even recently remarked that hedonic methods sometimes provide results very similar to the traditional matching models approach, particularly when models included in price index sample are replenished frequently. This paper briefly surveys the economic theory behind hedonic and traditional quality adjustment methods, and demonstrates that average price changes estimated by hedonic regressions differ from matched models estimation only because of the sum of regression residuals associated to disappearing and new models included in the sample. Thus, hedonic regressions including among the explanatory variables some indicators of the novelty and oldness of models provide exactly the same results of traditional methods. This fact casts some doubt on the overall effectiveness of hedonic methods in quality adjustment. The paper also focuses on that some economic and statistical hypotheses underlying hedonic methods possibly conflict with the assumptions and practices embodied in compiling the harmonised index of consumer prices for European countries.Consumer price index; Harmonised Index of Consumer Prices (HICP); Hedonic regressions; Matched models; Measurement of inflation; Quality adjustment

Predictions vs preliminary sample estimates

In general, rational economic agents are not in the position to wait for the statistical agencies disseminate the final results of the relevant surveys before making a decision, and have to make use of some model based predictions, even when agents are not assumedly forward looking. Thus, from the viewpoint of agents, predictions and preliminary results from surveys often compete against each other. Agents are aware to incur in a loss basing their decisions on predictions instead of sound statistical data, but the loss could be smaller than the one related to waiting for the dissemination of final data. Comparing the loss attached to predictions, on the one hand, and to possible preliminary estimate from incomplete samples, on the other, provides a broad guidance in deciding if and when statistical agencies should release preliminary and final estimates of the key variables. The main result of the analysis is that, in general, preliminary sample estimates are useful for the users only if they come from unexpectedly large sub-samples, even when the predictability of relevant variables is scarce. Nevertheless, the cost of delaying decisions for many economic agents may support the dissemination of early estimates of the main economic aggregates even if their accuracy is not fully satisfactory from a strict statistical viewpoint.Accuracy; Data Dissemination; Forecast; Preliminary Estimates; Timeliness

A simple model of discontinuous firm’s growth

Typically, firms change their size through a row of discrete leaps over time. Sunk costs, regulatory, financial and organizational constraints, talent distribution and other factors may explain this fact. However, firms tend to grow or fall discontinuously even if those inertial factors were removed. For instance, a very essential model of discontinuous growth can be based on a couple of assumptions concerning only technology and entrepreneurs’ strategy, that is: (a) in the short run, the firm’s equipment and organization provide the maximum profit only for a given production level, and diverging form it is costly; and (b) in the long run, the firm adjusts its size as if the current equipment had to be exploited until overall profit exceeds the profit expected from the new desired plant at the current production level. Combining the latter two hypotheses entails a number of testable consequences, usually regarded as nuisance facts within the traditional theoretical framework. First of all, an upper bound constraints both investment and disinvestment. Secondly, the profitability is not a continuous function of the firms’ size, but exhibits a number of peaks, each corresponding to a locally optimal size. Thirdly, firms tend to invest when profit approaches a local minimum, corresponding to the lowest profit claimed by the entrepreneur. Therefore, firm’s level data would prove only weak statistical relationships among profitability, output and investment. Finally, the distribution of firms by growth rate is multimodal since, within each sector, every firm typically adjusts its size through the same sequence of leaps. There are a number of analogies between the firm’s growth process predicted by the model and some physical phenomena explained by the quantum theory.Capacity utilization; Discontinuity; Firm’s size; Growth; Lumpy investment

Topology on the Lattice

We review the method developed in Pisa to determine the topological susceptibility in lattice QCD and present a collection of new and old results obtained by the method.Comment: 10 pages, 7 figures. Contribution to "Sense of Beauty in Physics - a volume in honour of Adriano Di Giacomo" (Pisa University Press, Pisa, 2006), on the occasion of his 70th birthda