The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

Alternatively, you can also download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link below.

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Download this PDF file Fullscreen Fullscreen Off

References

  1. Aurich, R.; Steiner, F. Periodic-orbit theory of the number variance $\Sigma^2(L)$ of strongly chaotic systems. Phys. D 82 (1995), no. 3, 266--287. MR1326559
  2. Barbour, A. D.; Hall, Peter. On the rate of Poisson convergence. Math. Proc. Cambridge Philos. Soc. 95 (1984), no. 3, 473--480. MR0755837
  3. Berry, M. V. The Bakerian lecture, 1987. Quantum chaology. Proc. Roy. Soc. London Ser. A 413 (1987), no. 1844, 183--198.MR0909277
  4. Berry, M. V. Semiclassical formula for the number variance of the Riemann zeros. Nonlinearity 1 (1988), no. 3, 399--407. MR0955621
  5. Berry, M. V.; Keating, J. P. The Riemann zeros and eigenvalue asymptotics. SIAM Rev. 41 (1999), no. 2, 236--266 (electronic). MR1684543
  6. Billingsley, Patrick. Convergence of probability measures. Second edition. Wiley Series in Probability and Statistics: Probability and Statistics. A Wiley-Interscience Publication. John Wiley & Sons, Inc., New York, 1999. x+277 pp. ISBN: 0-471-19745-9 MR1700749
  7. Bohigas, O.; Giannoni, M.-J.; Schmit, C. Characterization of chaotic quantum spectra and universality of level fluctuation laws. Phys. Rev. Lett. 52 (1984), no. 1, 1--4.MR0730191
  8. Costin, O. and Lebowitz, J. Gaussian fluctuations in random matrices}. Phys.Rev.Lett 75 (1995),69--72. Math Review number not available.
  9. Doob, J. L. Stochastic processes. John Wiley & Sons, Inc., New York; Chapman & Hall, Limited, London, 1953. viii+654 pp. MR0058896
  10. Feller, William. An introduction to probability theory and its applications. Vol. II. Second edition John Wiley & Sons, Inc., New York-London-Sydney 1971 xxiv+669 pp. MR0270403
  11. Goldstein, S.; Lebowitz, J. L.; Speer, E. R. Large deviations for a point process of bounded variability. Markov Process. Related Fields 12 (2006), no. 2, 235--256. MR2249630
  12. Gorostiza, Luis G.; Navarro, Reyla; Rodrigues, Eliane R. Some long-range dependence processes arising from fluctuations of particle systems. Acta Appl. Math. 86 (2005), no. 3, 285--308. MR2136367
  13. Lewis, T.; Govier, L. J. Some properties of counts of events for certain types of point process. J. Roy. Statist. Soc. Ser. B 26 1964 325--337. MR0178516
  14. Guhr, Thomas; Mller-Groeling, Axel. Spectral correlations in the crossover between GUE and Poisson regularity: on the identification of scales. Quantum problems in condensed matter physics. J. Math. Phys. 38 (1997), no. 4, 1870--1887. MR1450904
  15. Guhr, T. and Papenbrock, T. Spectral correlations in the crossover transition from a superposition of harmonic oscillators to the Gaussian unitary ensemble. Phys.Rev.E. 59 (1999), no. 1, 330--336. Math Review number not available.
  16. Isham, Valerie; Westcott, Mark. A self-correcting point process. Stochastic Process. Appl. 8 (1978/79), no. 3, 335--347. MR0535308
  17. Johansson, Kurt. Universality of the local spacing distribution in certain ensembles of Hermitian Wigner matrices. Comm. Math. Phys. 215 (2001), no. 3, 683--705.MR1810949
  18. Johansson, Kurt. Determinantal processes with number variance saturation. Comm. Math. Phys. 252 (2004), no. 1-3, 111--148. MR2103906
  19. Jones, Liza; O'Connell, Neil. Weyl chambers, symmetric spaces and number variance saturation. ALEA Lat. Am. J. Probab. Math. Stat. 2 (2006), 91--118 (electronic). MR2249664
  20. Kallenberg, Olav. Foundations of modern probability. Second edition. Probability and its Applications (New York). Springer-Verlag, New York, 2002. xx+638 pp. ISBN: 0-387-95313-2 MR1876169
  21. Luo, W.; Sarnak, P. Number variance for arithmetic hyperbolic surfaces. Comm. Math. Phys. 161 (1994), no. 2, 419--432.MR1266491
  22. Mandelbrot, Benoit B.; Van Ness, John W. Fractional Brownian motions, fractional noises and applications. SIAM Rev. 10 1968 422--437. MR0242239
  23. Mehta, Madan Lal. Random matrices. Third edition. Pure and Applied Mathematics (Amsterdam), 142. Elsevier/Academic Press, Amsterdam, 2004. xviii+688 pp. ISBN: 0-12-088409-7. MR2129906
  24. Samorodnitsky, Gennady; Taqqu, Murad S. Stable non-Gaussian random processes. Stochastic models with infinite variance. Stochastic Modeling. Chapman & Hall, New York, 1994. xxii+632 pp. ISBN: 0-412-05171-0. MR1280932
  25. Sato, Ken-iti. Lvy processes and infinitely divisible distributions. Translated from the 1990 Japanese original. Revised by the author. Cambridge Studies in Advanced Mathematics, 68. Cambridge University Press, Cambridge, 1999. xii+486 pp. ISBN: 0-521-55302-4. MR1739520
  26. Shanbhag, D. N.; Sreehari, M. On certain self-decomposable distributions. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 38 (1977), no. 3, 217--222.MR0436267
  27. Soshnikov, Alexander. Level spacings distribution for large random matrices: Gaussian fluctuations. Ann. of Math. (2) 148 (1998), no. 2, 573--617. MR1668559
  28. Soshnikov, A. Determinantal random point fields. (Russian) Uspekhi Mat. Nauk 55 (2000), no. 5(335), 107--160; translation in Russian Math. Surveys 55 (2000), no. 5, 923--975. MR1799012
  29. Soshnikov, Alexander B. Gaussian fluctuation for the number of particles in Airy, Bessel, sine, and other determinantal random point fields. J. Statist. Phys. 100 (2000), no. 3-4, 491--522. MR1788476
Bookmark and Share


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.