Fluctuation studies at the subnuclear level of matter: Evidence for stability, stationarity, and scaling

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 69, Issue 5, 2004, Pages 14-

  Liu Qin, ^a,b   Meng Ta chung, ^a,b  

^a CENTRAL CHINA NORMAL UNIVERSITY   (China)

^b FREIE UNIVERSITÄT BERLIN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33750447240     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.69.054026     Document Type: Article

References (15)

1. The theoretical scheme of such an approach can be found in textbooks. See, e.g., F. Halzen and A.D. Martin, Quarks and Leptons: An Introductory Course in Modern Particle Physics (Wiley and Sons, New York, 1984), and the references given therein. The most recent parametrizations can be found by tracing through the review talks given at the relevant international conferences on High Energy Physics and those on Heavy Ion Physics.
2. A. Einstein, Ann. Phys. (Leipzig) 17, 549 (1905). An English translation of his papers on this subject can, e.g., be found in A. Einstein (edited by R. Fürth and translated by A.D. Cowper), Investigations on the Theory of the Brownian Movement (Dover Publications, Inc., 1956).
3. L. Bachlier, Paris doctoral dissertation in mathematics, March 29, 1900, Annales de l’Ecole Normale Supérieure, Ser. 3, Vol. XVII (1900), pp. 21–86; Annales de l’Ecole Normale Supérieure, Ser. 3, Vol. XVIII (1901), pp. 143–210; Calcul des Probabilités (Gauthier-Villars, Paris, 1912); Le Jeu, la Chance et le Hasard (Paris, 1914 [reprinted up to 1929 at least]). See also, e.g., M.F.M. Osborne, Operations Research, Vol. VII (1959), p. 145. The modern authors have suggested that the original assumption of independent increment of (Formula presented) be replaced by the assumption of independent and Gaussian increments of (Formula presented)
4. See, e.g., B.B. Mandelbrot, Fractals and Scaling in Finance (Springer, Berlin, 1997), and the references given therein.
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10. See, e.g., R.E. Marshak, Conceptual Foundations of Modern Particle Physics (World Scientific, Singapore, 1993), p. 284.
11. See, e.g., A. Messiah (translated by G. M. Thmmer), Quantum Mechanics, Vol. I (North-Holland Publishing Company, Amsterdam, 1967).
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15. The definitions and theorems (including their proofs) can be found in monographs and text books on Probability Theory and Mathematical Statistics. See, e.g., W. Feller, An Introduction to Probability Theory and Its Applications, Vols. I, II (John Wiley and Sons, 1971); V.V. Uchaikin and V.M. Zolotarev, Chance and Stability: Stable Distributions and their Applications, Utrecht, The Netherlands (1999); J.P. Nolan, Stable Distribution Models for Heavy Tailed Data, http://academic2.american.edu/(Formula presented)jpnolan/home. html; WEI Zongshu, Gailülun Yu Shuli Tongji Jiaocheng (Probability Theory and Mathematical Statistics) (Gaodeng Jiaoyu Chubanshe, Beijing, China, 1983); MA Zhenhua et al., Xiandai Yingyong Shuxue Shouce: Gailü Tongji Yu Suiji Guocheng Juan (Handbook in Modern Applied Mathematics: Probability, Statistics and Random Processes Volumn) (Qinghua Daxue Chubanshe, Beijing, China, 2000).