Universal Fluctuations

The Phenomenology Of Hadronic Matter

By: Robert Botet, Marek Ploszajczak

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Paperback | 5 August 2002

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392 Pages

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The main purpose of this work is to present the appearance of universal limit probability laws in physics and their connection with the recently developed scaling theory of fluctuations. Arising from the probability theory and renormalization group methods, this approach has been proved to provide efficient investigative tools for the collective features that occur in any finite system. The mathematical background is self-contained and is formulated in terms which are easy to apply to the physical context. After illustrating the problem of anomalous diffusion, the book reviews recent advances in nuclear and high energy physics, where the limit laws are now recognized as being able to classify different phases of a system undergoing the pseudo-critical behaviour.

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?? the content of the book is much richer than simple applications in nuclear physics and in high-energy physics."

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Preface
Introduction	p. 1
Central Limit Theorem and Stable Laws	p. 7
Central limit theorem for broad distributions	p. 8
Stable laws for sum of uncorrelated variables	p. 13
Limit theorems for more complicated combinations of uncorrelated variables	p. 30
Two examples of physical applications	p. 39
Stable Laws for Correlated Variables	p. 45
Weakly and strongly correlated random variables	p. 46
Dyson's hierarchical model	p. 51
The renormalization group	p. 54
Self-similar probability distributions	p. 61
Critical systems	p. 66
Diffusion Problems	p. 75
Brownian motion	p. 75
Random walks	p. 81
Random walks with memory	p. 97
Random walk as a critical phenomenon	p. 106
Random walk as a self-similar process	p. 109
Poisson-Transform Distributions	p. 113
The class of poisson transforms	p. 114
Pascal distribution	p. 120
Stacy distribution	p. 127
Other examples of integral transforms	p. 135
KNO scaling limit	p. 135
Featuring the Correlations	p. 139
Moments and their generating function	p. 139
Some tools specific to the generating functions	p. 145
One example: the poisson distribution	p. 148
Composite distributions	p. 153
More about the pascal distribution	p. 158
Exclusive and Inclusive Densities	p. 163
Generalities and variables	p. 163
Cumulant correlation functions	p. 166
Scaled factorial moments	p. 168
Scaled factorial correlators and bin-split moments	p. 176
Scaled factorial cumulants	p. 178
Linked structure of the correlations	p. 183
Erraticity concept	p. 189
Bose-Einstein Correlations in Nuclear and Particle Physics	p. 199
Basic features of bose-einstein quantum statistical correlations	p. 200
Parametrization of the HBT data	p. 202
Bose-Einstein interference in models	p. 208
Idealized picture of independent particle production	p. 209
Bose-Einstein correlations in high-energy collisions	p. 214
Random Multiplicative Cascades	p. 221
Multiplicative cascade models	p. 222
Multifractals and intermittency	p. 227
Correlations in random cascading	p. 229
Non-ideal random cascades: the cut-off effect	p. 239
QCD cascade	p. 245
Random Cascades with Short-Scale Dissipation	p. 251
Basic features of the fragmentation-inactivation binary model	p. 254
Various approaches to the fragmentation-inactivation binary model	p. 257
Moment analysis of the fragmentation-inactivation binary equations	p. 261
Binary cascading with scale-dependent inactivation mechanism	p. 271
Perturbative quantum chromodynamics including inactivation mechanism	p. 277
Phenomenology of the multiplicity distributions in e[superscript +]e[superscript -] reactions	p. 281
Fluctuations of the Order Parameter	p. 285
Order parameter fluctuations in self-similar systems	p. 286
Example of the non-critical model	p. 290
Mean-field critical model: the Landau-Ginzburg model	p. 293
Example of the critical model: the potts model	p. 297
Reversible aggregation: example of the percolation model	p. 300
Irreversible aggregation: example of the smoluchowski kinetic model	p. 308
Off-equilibrium fragmentation	p. 317
Universal Fluctuations in Nuclear and Particle Physics	p. 321
Phenomenology of high energy collisions in the scaled factorial moments analysis	p. 322
[Delta]-scaling in [actual symbol not reproducible] collisions?	p. 330
Universal fluctuations in excited nuclear matter	p. 335
Final Remarks	p. 345
Bibliography	p. 349
Index	p. 363
Table of Contents provided by Blackwell. All Rights Reserved.

Universal Fluctuations

The Phenomenology Of Hadronic Matter

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

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