Contents -- Preface -- Chapter 1 Introduction -- Chapter 2 Central Limit Theorem and Stable Laws -- 2.1 Central limit theorem for broad distributions -- 2.2 Stable laws for sum of uncorrelated variables -- 2.3 Limit theorems for more complicated combinations of uncorrelated variables -- 2.4 Two examples of physical applications -- Chapter 3 Stable Laws for Correlated Variables -- 3.1 Weakly and strongly correlated random variables -- 3.2 Dyson's hierarchical model -- 3.3 The renormalization group -- 3.4 Self-similar probability distributions -- 3.5 Critical systems -- Chapter 4 Diffusion Problems -- 4.1 Brownian motion -- 4.2 Random walks -- 4.3 Random walks with memory -- 4.4 Random walk as a critical phenomenon -- 4.5 Random walk as a self-similar process -- Chapter 5 Poisson-Transform Distributions -- 5.1 The class of Poisson transforms -- 5.2 Pascal distribution -- 5.3 Stacy distribution -- 5.4 Other examples of integral transforms -- 5.5 KNO scaling limit -- Chapter 6 Featuring the Correlations -- 6.1 Moments and their generating function -- 6.2 Some tools specific to the moment generating functions -- 6.4 Infinitely divisible distribution functions -- 6.5 Composite distributions -- 6.6 More about the Pascal distribution -- Chapter 7 Exclusive and Inclusive Densities -- 7.1 Generalities and variables -- 7.2 Cumulant correlation functions -- 7.3 Scaled factorial moments -- 7.4 Scaled factorial correlators and bin-split moments -- 7.5 Scaled factorial cumulants -- 7.6 Linked structure of the correlations -- 7.7 Erraticity concept -- Chapter 8 Bose-Einstein Correlations in Nuclear and Particle Physics -- 8.1 Basic features of Bose-Einstein quantum statistical correlations -- 8.2 Parametrization of the HBT data -- 8.3 Bose-Einstein interference in models.

8.4 Idealized picture of independent particle production -- 8.5 Bose-Einstein correlations in high-energy collisions -- Chapter 9 Random Multiplicative Cascades -- 9.1 Multiplicative cascade models -- 9.2 Multifractals and intermittency -- 9.3 Correlations in random cascading -- 9.4 Non-ideal random cascades: the cut-off effect -- 9.5 QCD cascade -- Chapter 10 Random Cascades with Short-Scale Dissipation -- 10.1 Basic features of the fragmentation-inactivation binary model -- 10.2 Various approaches to the fragmentation-inactivation binary model -- 10.3 Moment analysis of the fragmentation-inactivation binary equations -- 10.4 Binary cascading with scale-dependent inactivation mechanism -- 10.5 Perturbative quantum chromodynamics including inactivation mechanism -- 10.6 Phenomenology of the multiplicity distributions in e+e- reactions -- Chapter 11 Fluctuations of the Order Parameter -- 11.1 Order parameter fluctuations in self-similar systems -- 11.2 Example of the non-critical model -- 11.3 Mean-field critical model: the Landau-Ginzburg model -- 11.4 Example of the critical model: the Potts model -- 11.5 Reversible aggregation: example of the percolation model -- 11.6 Irreversible aggregation: example of the Smoluchowski kinetic model -- 11.7 Off-equilibrium fragmentation -- Chapter 12 Universal Fluctuations in Nuclear and Particle Physics -- 12.1 Phenomenology of high energy collisions in the scaled factorial moments analysis -- 12.2 ∆-scaling in pp collisions? -- 12.3 Universal fluctuations in excited nuclear matter -- Chapter 13 Final Remarks -- Bibliography -- Index.