On the correlation structure of some random point processes on the line

Physica A: Statistical Mechanics and its Applications

Volumn 387, Issue 4, 2008, Pages 725-744

  de Coninck, Joël ^a   Dunlop, François ^b   Huillet, Thierry ^b  

^a UNIVERSITY OF MONS   (Belgium)

^b UNIVERSITÉ DE CERGY PONTOISE   (France)

Author keywords

Anomalous fluctuations; Correlation functions; Determinantal, permanental and renewal point processes on the line; Random systems; Sub and super homogeneous point processes

Indexed keywords

FERMIONS; NUMBER THEORY; POISSON DISTRIBUTION;

ANOMALOUS FLUCTUATIONS; BOUNDED SPACINGS VARIANCE; CORRELATION FUNCTIONS; RANDOM SYSTEMS;

CORRELATION METHODS;

EID: 36649017719     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2007.10.018     Document Type: Article

References (23)

1. Bhatia R. Infinitely divisible matrices. Amer. Math. Monthly 113 3 (2006) 221-235
2. Costin O., and Lebowitz J.L. Gaussian fluctuation in random matrices. Phys. Rev. Lett. 75 (1995) 69-72
3. Costin O., and Lebowitz J.L. On the construction of particle distributions with specified single and pair densities. J. Phys. Chem. B 108 51 (2004) 19614-19618
4. Daley D.J., and Vesilo R. Long range dependence of point processes, with queueing examples. Stochastic Process. Appl. 70 2 (1997) 265-282
5. Daley D.J., and Vere-Jones D. An introduction to the theory of point processes. Springer Series in Statistics (1988), Springer-Verlag, New York
6. Feller W. An Introduction to Probability Theory and its Applications vol. 2 (1971), Wiley, New York
7. FitzGerald C.H., and Horn R.A. On fractional Hadamard powers of positive definite matrices. J. Math. Anal. Appl. 61 3 (1977) 633-642
8. Gabrielli A., Joyce M., and Labini F.S. Glass-like universe: Real-space correlation properties of standard cosmological models. Phys. Rev. D 65 (2002) 083523
9. Goldstein S., Lebowitz J.L., and Speer E.R. Large deviations for a point process of bounded variability. Markov Process. Related Fields 12 2 (2006) 235-256
10. Godrèche C., and Oguey C. Construction of average lattices for quasiperiodic structures by the section method. J. Phys. France 51 (1990) 21-27
11. Gabrielli A., and Torquato S. Voronoi and void statistics for super-homogeneous point processes. Phys. Rev. E 70 (2004) 041105
12. Huillet T. On Linnik's continuous-time random walks. J. Phys. A 33 14 (2000) 2631-2652
13. Huillet T. Renewal processes and the Hurst effect. J. Phys. A 35 20 (2002) 4395-4412
14. Hough J.B., Krishnapur M., Peres Y., and Virág B. Determinantal processes and independence. Probab. Surv. 3 (2006) 206-229
15. Johansson K. Random matrices and determinantal processes. Les Houches Series Session LXXXIII (2006), Mathematical Statistical Physics, Elsevier
16. T. Kuna, J.L. Lebowitz, E.R. Speer, Realizability of point processes, Mathematical Physics Preprint Archive, 06-369, 2006
17. Lim S.C., and Li M. A generalized Cauchy process and its application to relaxation phenomena. J. Phys. A 39 (2006) 2935-2951
18. Macchi O. The coincidence approach to stochastic point processes. Adv. in Appl. Probab. 7 (1975) 83-122
19. Meeron E., and Siegert A.J.F. Statistical mechanics of hard particle systems. J. Chem. Phys. 48 (1968) 3139-3155
20. Soshnikov A. Determinantal random point fields. Uspekhi Mat. Nauk 55 5(335) (2000) 107-160 Translation in Russian Math. Surveys, 55 (5) 2000, 923-975 (in Russian)
21. Steutel F.W., and van Harn K. Infinite divisibility of probability distributions on the real line. Monographs and Textbooks in Pure and Applied Mathematics vol. 259 (2004), Marcel Dekker, Inc., New York
22. Torquato S., and Stillinger F.H. Local density fluctuations, hyperuniformity and order metrics. Phys. Rev. E 68 (2003) 041113
23. Tracy C.A., and Widom H. Level-spacing distributions and the Airy kernel. Phys. Lett. B 305 1-2 (1993) 115-118