Uniform asymptotics of the coefficients of unitary moment polynomials

Keating and Snaith showed that the $2k^{th}$ absolute moment of the characteristic polynomial of a random unitary matrix evaluated on the unit circle is given by a polynomial of degree $k^2$. In this article, uniform asymptotics for the coefficients of that polynomial are derived, and a maximal coefficient is located. Some of the asymptotics are given in explicit form. Numerical data to support these calculations are presented. Some apparent connections between random matrix theory and the Riemann zeta function are discussed.Comment: 31 pages, 1 figure, 2 tables. A few minor misprints fixe

Hospitalizations during the last months of life of nursing home residents: a retrospective cohort study from Germany

BACKGROUND: To describe hospitalisations of nursing home (NH) residents in Germany during their last months of life. METHODS: Retrospective cohort study on 792 NH residents in the Rhine-Neckar region in South-West Germany, newly institutionalized in the year 2000, who died until the study end (December 2001). Baseline variables were derived from a standardized medical examination routinely conducted by the medical service of the health care insurance plans in Germany. Information on hospitalisations and deaths was extracted form records of the pertinent health insurance plans. RESULTS: NH residents who died after NH stay of more than 1 year spent 5.8% of their last year of life in hospitals. Relative time spent in hospitals increased from 5.2% twelve months before death (N = 139 persons) to 24.1% in their last week of life (N = 769 persons). No major differences could be observed concerning age, gender or duration of stay in NH. Overall, 229 persons (28.9%) died in hospital. Among these, the last hospital stay lasted less than 3 days for 76 persons (31.9%). Another 25 persons (3.2%) died within three days after hospital discharge. CONCLUSION: Our study indicates that proximity of death is the most important driver of health care utilization among NH residents. The relation of age or gender to health care expenditures seem to be weak once time to death is controlled for. Duration of NH stay does not markedly change rates of hospitalisation during the last months of life

Asymptotic Estimates for Generalized Stirling Numbers

Uniform asymptotic expansions are given for the Stirling numbers of the first kind for integral arguments and for the second kind as defined for real arguments by Flajolet and Prodinger. The logconcavity of the resulting real valued function of Flajolet and Prodinger is established for a range including the classical integral domain