Kronecker's Double Series and Exact Asymptotic Expansion for Free Models of Statistical Mechanics on Torus

For the free models of statistical mechanics on torus, exact asymptotic expansions of the free energy, the internal energy and the specific heat in the vicinity of the critical point are found. It is shown that there is direct relation between the terms of the expansion and the Kronecker's double series. The latter can be expressed in terms of the elliptic theta-functions in all orders of the asymptotic expansion.Comment: REVTeX, 22 pages, this is expanded version which includes exact asymptotic expansions of the free energy, the internal energy and the specific hea

Electron transport and optical properties of shallow GaAs/InGaAs/GaAs quantum wells with a thin central AlAs barrier

Shallow GaAs/InGaAs/GaAs quantum well structures with and without a three monolayer thick AlAs central barrier have been investigated for different well widths and Si doping levels. The transport parameters are determined by resistivity measurements in the temperature range 4-300 K and magnetotransport in magnetic fields up to 12 T. The (subband) carrier concentrations and mobilities are extracted from the Hall data and Shubnikov-de Haas oscillations. We find that the transport parameters are strongly affected by the insertion of the AlAs central barrier. Photoluminescence spectra, measured at 77 K, show an increase of the transition energies upon insertion of the barrier. The transport and optical data are analyzed with help of self-consistent calculations of the subband structure and envelope wave functions. Insertion of the AlAs central barrier changes the spatial distribution of the electron wave functions and leads to the formation of hybrid states, i.e. states which extend over the InGaAs and the delta-doped layer quantum wells.Comment: 14 pages, pdf fil

Multifractality in Time Series

We apply the concepts of multifractal physics to financial time series in order to characterize the onset of crash for the Standard & Poor's 500 stock index x(t). It is found that within the framework of multifractality, the "analogous" specific heat of the S&P500 discrete price index displays a shoulder to the right of the main peak for low values of time lags. On decreasing T, the presence of the shoulder is a consequence of the peaked, temporal x(t+T)-x(t) fluctuations in this regime. For large time lags (T>80), we have found that C_{q} displays typical features of a classical phase transition at a critical point. An example of such dynamic phase transition in a simple economic model system, based on a mapping with multifractality phenomena in random multiplicative processes, is also presented by applying former results obtained with a continuous probability theory for describing scaling measures.Comment: 22 pages, Revtex, 4 ps figures - To appear J. Phys. A (2000

Programming languages and opportunities they offer to the statistical community

Naeve P. Programming languages and opportunities they offer to the statistical community. In: Prohorov YA, Sazonov VV, eds. Proceedings of the 1st [First] World Congress of the Bernoulli Society: Tashkent, USSR, 8-14 September 1986. Vol vol. 1: Probability theory and applications. Utrecht: VNU Science Pr.; 1986: 779-792

Bounds For Characteristic Functions Of Polynomials In Asymptotically Normal Variables

Let f be a polynomial in k variables and Sn be a normed sum of independent identically distributed random vectors X 1 ; X 2 ; : : : ; Xn taking values in R k . Upper bounds for jE expfit f(Sn )gj are derived provided that either the distribution of X 1 has a nondegenerate discrete component or the distribution of Sn 0 has an absolutely continuous component for some n 0 . The dependence on t and n is given in an explicit form. The proofs are based on some number-theoretic results