The Time-Energy Uncertainty Relation

The time energy uncertainty relation has been a controversial issue since the advent of quantum theory, with respect to appropriate formalisation, validity and possible meanings. A comprehensive account of the development of this subject up to the 1980s is provided by a combination of the reviews of Jammer (1974), Bauer and Mello (1978), and Busch (1990). More recent reviews are concerned with different specific aspects of the subject. The purpose of this chapter is to show that different types of time energy uncertainty relation can indeed be deduced in specific contexts, but that there is no unique universal relation that could stand on equal footing with the position-momentum uncertainty relation. To this end, we will survey the various formulations of a time energy uncertainty relation, with a brief assessment of their validity, and along the way we will indicate some new developments that emerged since the 1990s.Comment: 33 pages, Latex. This expanded version (prepared for the 2nd edition of "Time in quantum mechanics") contains minor corrections, new examples and pointers to some additional relevant literatur

Asset Pricing Model Specification and the Term Structure Evidence

In this paper, a set of tests of models of relative capital asset pricesis developed. The tests are used to examine how well the models explain maturity premiums on Government bonds, though they are perfectly general and hence could be applied to stocks or other assets. Allowance is made in the tests for the nonobservability of investors' optimal per capita consumption (or expected marginal utility). It is found that the returns on Government bonds bear a systematic risk which is better measured by their covariability with aggregate per capita consumption than with the returns on the NYSE stock market index, the latter being the surrogate-wealth portfolio typically used to measure risk in the traditional Sharpe-Lintner-Mossin CAPM.

Orthogonal polynomial ensembles in probability theory

We survey a number of models from physics, statistical mechanics, probability theory and combinatorics, which are each described in terms of an orthogonal polynomial ensemble. The most prominent example is apparently the Hermite ensemble, the eigenvalue distribution of the Gaussian Unitary Ensemble (GUE), and other well-known ensembles known in random matrix theory like the Laguerre ensemble for the spectrum of Wishart matrices. In recent years, a number of further interesting models were found to lead to orthogonal polynomial ensembles, among which the corner growth model, directed last passage percolation, the PNG droplet, non-colliding random processes, the length of the longest increasing subsequence of a random permutation, and others. Much attention has been paid to universal classes of asymptotic behaviors of these models in the limit of large particle numbers, in particular the spacings between the particles and the fluctuation behavior of the largest particle. Computer simulations suggest that the connections go even farther and also comprise the zeros of the Riemann zeta function. The existing proofs require a substantial technical machinery and heavy tools from various parts of mathematics, in particular complex analysis, combinatorics and variational analysis. Particularly in the last decade, a number of fine results have been achieved, but it is obvious that a comprehensive and thorough understanding of the matter is still lacking. Hence, it seems an appropriate time to provide a surveying text on this research area.Comment: Published at http://dx.doi.org/10.1214/154957805100000177 in the Probability Surveys (http://www.i-journals.org/ps/) by the Institute of Mathematical Statistics (http://www.imstat.org

On the Returns to Occupational Qualification in Terms of Subjective and Objective Variables: A GEE-type Approach to the Estimation of Two-Equation Panel Models

This article proposes an estimation approach for panel models with mixed continuous and ordered categorical outcomes based on generalized estimating equations for the mean and pseudo-score equations for the covariance parameters. A numerical study suggests that efficiency can be gained as concerns the mean parameter estimators by using individual covariance matrices in the estimating equations for the mean parameters. The approach is applied to estimate the returns to occupational qualification in terms of income and perceived job security in a nine-year period based on the German Socio-Economic Panel (SOEP). To compensate for missing data, a combined multiple imputation/weighting approach is adopted.Generalized estimating equations, mean and covariance model, multiple imputation, pseudo-score equations, status inconsistency, weighting