Spectra of Sparse Random Matrices

We compute the spectral density for ensembles of of sparse symmetric random matrices using replica, managing to circumvent difficulties that have been encountered in earlier approaches along the lines first suggested in a seminal paper by Rodgers and Bray. Due attention is payed to the issue of localization. Our approach is not restricted to matrices defined on graphs with Poissonian degree distribution. Matrices defined on regular random graphs or on scale-free graphs, are easily handled. We also look at matrices with row constraints such as discrete graph Laplacians. Our approach naturally allows to unfold the total density of states into contributions coming from vertices of different local coordination.Comment: 22 papges, 8 figures (one on graph-Laplacians added), one reference added, some typos eliminate

Tax rates, governance, and the informal economy in high-income countries

This paper studies the mechanisms behind the informal economy in high-income countries. About 16.3% of output in high-income OECD countries was produced informally in 2001-02. In a recent paper Davis and Henrekson [2004] show that there exists a positive relationship between tax rates and the informal economy for high-income OECD countries. Existing models of the informal economy mostly focus on developing countries. To account for the informal economy in high-income countries, build a model economy, following Lucas [1978], in which agents of different managerial abilities decide to become workers, managers of informal firms, or managers of formal firms. In contrast to formal managers, managers of informal firms do not pay taxes but run the risk of getting caught, taxed, and fined. A calibrated version of the model economy is able to generate the observed differences in informal economy of 21 high-income countries. Although tax rates are crucial for explaining the observed differences in informal economy, the quality of governance, the extent to which these tax rates are enforced, also plays an important role. Policy experiments show that by improving the enforcement of their tax policies countries can reduce informality. A smaller informal economy is accompanied by larger firms and higher productivity

Disentangling Giant Component and Finite Cluster Contributions in Sparse Matrix Spectra

We describe a method for disentangling giant component and finite cluster contributions to sparse random matrix spectra, using sparse symmetric random matrices defined on Erdos-Renyi graphs as an example and test-bed.Comment: 7 pages, 2 multi-part figure