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9789810248987

Universal Fluctuations : The Phenomenology of Hadronic Matter

by ; ;
  • ISBN13:

    9789810248987

  • ISBN10:

    9810248989

  • Format: Hardcover
  • Copyright: 2002-08-01
  • Publisher: WORLD SCIENTIFIC PUB CO INC
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Supplemental Materials

What is included with this book?

Summary

The main purpose of this book is to present, in a comprehensive and progressive way, the appearance of universal limit probability laws in physics, and their connection with the recently developed scaling theory of fluctuations.

Table of Contents

Preface vii
Introduction
1(6)
Central Limit Theorem and Stable Laws
7(38)
Central limit theorem for broad distributions
8(5)
Central limit theorem for the sum of uncorrelated variables
8(5)
Stable laws for sum of uncorrelated variables
13(17)
The stability problem
13(4)
Complete solution of the stability problem for uncorrelated variables
17(1)
The ensemble of one-dimensional stable distributions
17(1)
Alternative formulas for the stable distributions
17(1)
Range of values for μ
18(1)
Range of values for β
19(1)
Gaussian distribution as a stable law
20(1)
Moments of the stable distributions
20(2)
Explicit examples of stable distributions
22(1)
Symmetric stable distributions (β = 0)
22(2)
Asymmetric stable distributions (β = 1)
24(1)
The reciprocity relation for stable distributions
25(1)
The tail of stable distributions
26(1)
Moments of stable distributions
26(1)
Asymptotically stable laws - domains of attraction
27(2)
The concept of the Δ-scaling
29(1)
Limit theorems for more complicated combinations of uncorrelated variables
30(9)
Product of uncorrelated variables
30(4)
The Kesten variable
34(1)
The Gumbel distribution
35(3)
The arc-sine law
38(1)
Two examples of physical applications
39(6)
The Holtsmark problem
39(2)
The stretched-exponential relaxation
41(4)
Stable Laws for Correlated Variables
45(30)
Weakly and strongly correlated random variables
46(5)
Correlated random Gaussian processes
47(2)
Taqqu's reduction theorem
49(1)
Rosenblatt's model
50(1)
Dyson's hierarchical model
51(3)
The renormalization group
54(7)
The renormalization group and the stability problem
55(1)
Scaling features
56(1)
ε-expansion
57(2)
Multiplicative structure of the renormalization group
59(2)
Self-similar probability distributions
61(5)
Self-similar processes
61(1)
Euler theorem
62(1)
Self-similarity of fractals in the renormalization group approach
63(1)
The power spectral density function
64(1)
Δ-scaling framework
65(1)
Critical systems
66(9)
Anomalous dimension
67(1)
First scaling
68(2)
Second scaling
70(1)
Δ-scaling
71(2)
Studies of criticality in finite systems
73(2)
Diffusion Problems
75(38)
Brownian motion
75(6)
Fick's representation
75(2)
Ornstein-Uhlenbeck representation
77(2)
Fokker-Planck representation
79(2)
Random walks
81(16)
Gaussian random walks and Gaussian Levy flights
81(3)
St. Petersburg paradox
84(2)
Non-Gaussian Levy flights
86(1)
Anomalous diffusion
86(3)
Continuous Levy flights
89(1)
Return to the origin of the random walk
90(2)
Random walk in a random environment
92(4)
Sinai billiard
96(1)
Random walks with memory
97(9)
Random walks with Gaussian memory
97(2)
Fractional Brownian motion
99(3)
Flory's approach for linear polymers
102(4)
Random walk as a critical phenomenon
106(3)
Criticality of the Brownian motion
106(1)
Criticality of the Levy flight
107(1)
Criticality of the self-avoiding walk
108(1)
Random walk as a self-similar process
109(4)
Self-similarity of the Brownian motion
109(1)
Anomalous diffusion in the fractal space
110(3)
Poisson-Transform Distributions
113(26)
The class of poisson transforms
114(6)
General functional relations for the Poisson transforms
116(1)
Examples of Poisson transforms
117(2)
Generating function for the Poisson transforms
119(1)
Pascal distribution
120(7)
Definition and moments of the Pascal distribution
121(1)
Recurrence relations for the Pascal distribution
121(2)
Limit cases of the Poisson distribution
123(1)
Stability of the Pascal distribution
123(2)
Origins of the Pascal distribution
125(1)
Stochastic differential equation leading to the Pascal distribution
126(1)
Stacy distribution
127(8)
The generalized Gamma distribution and its moments
128(1)
Langevin and Fokker-Planck equations leading to the generalized Gamma function
129(1)
One-dimensional Langevin equation with the multiplicative noise
130(1)
Explicit physical processes leading to the one-dimensional Langevin equation with the multiplicative noise
131(1)
Solution of the one-dimensional Langevin equation with the multiplicative noise
132(1)
The limit case with vanishing random force
133(2)
Other examples of integral transforms
135(1)
KNO scaling limit
135(4)
Extension of the KNO scaling rule
136(3)
Featuring the Correlations
139(24)
Moments and their generating function
139(7)
Moments
140(1)
Cumulant moments
140(1)
Factorial moments
141(1)
Cumulant factorial moments
142(1)
Normalized moments
142(2)
Bunching parameters
144(1)
Combinants
144(1)
Existence of the generating functions
145(1)
Some tools specific to the moment generating functions
146(2)
Singularities of the moment generating function
146(1)
The Stieltjes series
147(1)
One example: the poisson distribution
148(3)
Infinitely divisible distribution functions
151(2)
Truncating the multiplicity distribution
153(1)
Composite distributions
153(5)
Conditional and joint probabilities
154(1)
Clan structures
155(3)
More about the pascal distribution
158(5)
The limiting forms
159(2)
High-energy phenomenology
161(2)
Exclusive and Inclusive Densities
163(36)
Generalities and variables
163(3)
Cumulant correlation functions
166(2)
Scaled factorial moments
168(8)
Intermittency with the scaled factorial moments
169(2)
Correcting for the shape of the one-particle distribution and the lack of the translational invariance
171(1)
Unphysical correlations due to the mixing of events of different multiplicities
172(1)
Dimensional projection
173(3)
Scaled factorial correlators and bin-split moments
176(2)
Scaled factorial cumulants
178(5)
Correlation integral
180(3)
Linked structure of the correlations
183(6)
Linked pair approximation
183(1)
Linked approximation in the conformal theory
184(2)
Linked approximation for the Δ-scaling
186(1)
Counts and their fluctuations
187(2)
Erraticity concept
189(10)
Wavelet representation
192(3)
Simple examples of wavelets
195(4)
Bose-Einstein Correlations in Nuclear and Particle Physics
199(22)
Basic features of bose-einstein quantum statistical correlations
200(2)
Parametrization of the HBT data
202(6)
The space-time structure of the multiparticle system
204(2)
HBT measurements in condensed matter and atomic physics
206(2)
Bose-Einstein interference in models
208(1)
Idealized picture of independent particle production
209(5)
Monte-Carlo simulations
212(2)
Bose-Einstein correlations in high-energy collisions
214(7)
Higher order cumulants in pp collisions
214(3)
Small-scale Bose-Einstein correlations
217(2)
Density dependence of the correlations
219(2)
Random Multiplicative Cascades
221(30)
Multiplicative cascade models
222(5)
Weak intermittency regime
223(2)
Strong intermittency regime
225(1)
Regularization of the scaled factorial moments in the strong intermittency limit
226(1)
Multifractals and intermittency
227(2)
Correlations in random cascading
229(10)
Some examples of the branching generating functions
235(1)
Link to the multifractal formalism
236(2)
Relation between branching generating function and multifractal mass exponents
238(1)
Non-ideal random cascades: the cut-off effect
239(6)
Multiscaling dependence on the cut-off parameters
240(3)
α-model with the cut-off at small scales
243(2)
QCD cascade
245(6)
Random Cascades with Short-Scale Dissipation
251(34)
Basic features of the fragmentation-inactivation binary model
254(3)
Shattering transition
255(1)
Scale-independent dissipation effects: the phase diagramme
256(1)
Various approaches to the fragmentation-inactivation binary model
257(4)
Fragmentation-inactivation binary model as a random multiplicative cascade
257(1)
Fragmentation-inactivation binary model as a mean-field branching process
258(1)
Cascade equation for the multiplicity evolution
259(1)
Master equation
260(1)
Moment analysis of the fragmentation-inactivation binary equations
261(10)
General equations for the factorial moments and cumulant moments
261(1)
Moments of the multiplicity distribution at the transition line
262(1)
Brand - Schenzle fragmentation domain (pF > 1/2, α > --1)
263(2)
Marginal case : pF = 1/2, α > --1
265(1)
Cayley fragmentation domain: pF < 1/2, α > --1
266(2)
Evaporative fragmentation domain: pF > 0, α < --1
268(2)
Structure of higher-order cumulant correlations at the transitional line
270(1)
Binary cascading with scale-dependent inactivation mechanism
271(6)
First example : binary cascading with α = --1 and the Gaussian inactivation
272(3)
Second example: binary fragmentation with α = +1 and the Gaussian inactivation
275(1)
Δ-scaling vs value of exponent τ
275(1)
Multiplicity fluctuations in different physical systems and in the binary fragmentation
276(1)
Perturbative quantum chromodynamics including inactivation mechanism
277(4)
Multiplicity distributions in the dissipative gluodynamics
280(1)
Phenomenology of the multiplicity distributions in e+e- reactions
281(4)
Fluctuations of the Order Parameter
285(36)
Order parameter fluctuations in self-similar systems
286(4)
The anomalous dimension
286(2)
Critical cluster-size
288(1)
Note about the correct order parameter
289(1)
Example of the non-critical model
290(3)
The weight functions
290(1)
Check of the linked pair approximation
290(1)
Second scaling law
291(1)
Note about the average size-distribution
292(1)
Mean-field critical model: the Landau-Ginzburg model
293(4)
Landau-Ginzburg free energy
293(1)
Distribution of the extensive order parameter
293(1)
First scaling at the pseudo-critical point
294(1)
Gaussian first scaling in the disordered phase
295(1)
Second scaling in the ordered phase
295(1)
Correlation pattern in the Landau-Ginzburg theory
296(1)
Example of the critical model: the potts model
297(3)
Scaling laws for the order-parameter distribution
298(2)
Reversible aggregation: example of the percolation model
300(8)
Order parameter in the percolation on the Bethe lattice
301(3)
The three-dimensional percolation model
304(1)
Multiplicity distributions
304(1)
Order-parameter distribution
304(1)
Shifted order parameter
304(1)
Outside of the critical point
305(2)
Close to the critical point
307(1)
Irreversible aggregation: example of the smoluchowski kinetic model
308(9)
Basic behaviour of the order parameter
308(2)
Scalings of the order-parameter distributions
310(1)
Tails of the scaling functions
311(1)
Scaling for the shifted order parameter
312(1)
Origin of fluctuations in non-equilibrium aggregation
313(1)
Argument of Van Kampen
313(2)
Gelling systems
315(1)
Scaling of the second moments for gelling systems
315(2)
Non-gelling systems
317(1)
Off-equilibrium fragmentation
317(4)
Universal Fluctuations in Nuclear and Particle Physics
321(24)
Phenomenology of high energy collisions in the scaled factorial moments analysis
322(8)
Nonsingular parts in the correlations
322(1)
Choice of the variables
323(1)
General phenomenology and experimental results
324(4)
Self-similarity or self-affinity in multiparticle production?
328(1)
Self-affine analysis of π+ / K+p data
329(1)
Δ-scaling in pp collisions?
330(5)
Aggregation scenario for pp and AA collisions?
333(2)
Universal fluctuations in excited nuclear matter
335(10)
Δ-scaling in nucleus-nucleus collisions in the Fermi energy domain
337(8)
Final Remarks
345(4)
Bibliography 349(14)
Index 363

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