Universal Fluctuations: The Phenomenology of Hadronic Matter Book

	Preface
Ch. 1	Introduction	1
Ch. 2	Central Limit Theorem and Stable Laws	7
2.1	Central limit theorem for broad distributions	8
2.2	Stable laws for sum of uncorrelated variables	13
2.3	Limit theorems for more complicated combinations of uncorrelated variables	30
2.4	Two examples of physical applications	39
Ch. 3	Stable Laws for Correlated Variables	45
3.1	Weakly and strongly correlated random variables	46
3.2	Dyson's hierarchical model	51
3.3	The renormalization group	54
3.4	Self-similar probability distributions	61
3.5	Critical systems	66
Ch. 4	Diffusion Problems	75
4.1	Brownian motion	75
4.2	Random walks	81
4.3	Random walks with memory	97
4.4	Random walk as a critical phenomenon	106
4.5	Random walk as a self-similar process	109
Ch. 5	Poisson-Transform Distributions	113
5.1	The class of poisson transforms	114
5.2	Pascal distribution	120
5.3	Stacy distribution	127
5.4	Other examples of integral transforms	135
5.5	KNO scaling limit	135
Ch. 6	Featuring the Correlations	139
6.1	Moments and their generating function	139
6.2	Some tools specific to the generating functions	145
6.3	One example: the poisson distribution	148
6.5	Composite distributions	153
6.6	More about the pascal distribution	158
Ch. 7	Exclusive and Inclusive Densities	163
7.1	Generalities and variables	163
7.2	Cumulant correlation functions	166
7.3	Scaled factorial moments	168
7.4	Scaled factorial correlators and bin-split moments	176
7.5	Scaled factorial cumulants	178
7.6	Linked structure of the correlations	183
7.7	Erraticity concept	189
Ch. 8	Bose-Einstein Correlations in Nuclear and Particle Physics	199
8.1	Basic features of bose-einstein quantum statistical correlations	200
8.2	Parametrization of the HBT data	202
8.3	Bose-Einstein interference in models	208
8.4	Idealized picture of independent particle production	209
8.5	Bose-Einstein correlations in high-energy collisions	214
Ch. 9	Random Multiplicative Cascades	221
9.1	Multiplicative cascade models	222
9.2	Multifractals and intermittency	227
9.3	Correlations in random cascading	229
9.4	Non-ideal random cascades: the cut-off effect	239
9.5	QCD cascade	245
Ch. 10	Random Cascades with Short-Scale Dissipation	251
10.1	Basic features of the fragmentation-inactivation binary model	254
10.2	Various approaches to the fragmentation-inactivation binary model	257
10.3	Moment analysis of the fragmentation-inactivation binary equations	261
10.4	Binary cascading with scale-dependent inactivation mechanism	271
10.5	Perturbative quantum chromodynamics including inactivation mechanism	277
10.6	Phenomenology of the multiplicity distributions in e[superscript +]e[superscript -] reactions	281
Ch. 11	Fluctuations of the Order Parameter	285
11.1	Order parameter fluctuations in self-similar systems	286
11.2	Example of the non-critical model	290
11.3	Mean-field critical model: the Landau-Ginzburg model	293
11.4	Example of the critical model: the potts model	297
11.5	Reversible aggregation: example of the percolation model	300
11.6	Irreversible aggregation: example of the smoluchowski kinetic model	308
11.7	Off-equilibrium fragmentation	317
Ch. 12	Universal Fluctuations in Nuclear and Particle Physics	321
12.1	Phenomenology of high energy collisions in the scaled factorial moments analysis	322
12.2	[Delta]-scaling in [actual symbol not reproducible] collisions?	330
12.3	Universal fluctuations in excited nuclear matter	335
Ch. 13	Final Remarks	345
	Bibliography	349
	Index	363