# Noise Theory and Application to Physics:

From Fluctuations to Information
Springer, Apr 27, 2004 - Science - 288 pages
In many situations, physical quantities are perturbed or evolve in a not fully predictable way. We then speak about noise or fluctuations and we are generally faced to different questions such as: What are the correct physical models to describe them? What are the most practical mathematical tools to deal with them? How can relevant information be extracted in the presence of noise? Noise theory and application to physics provides a precise description of the theoretical background and practical tools for noise and fluctuation analyses. It not only introduces basic mathematical descriptions and properties of noise and fluctuations but also discusses the physical origin of different noise models and presents some statistical methods which optimize measurements in the presence of such fluctuations. Noise theory and application to physics investigates a number of ideas about noise and fluctuations in a single book in relation with probability and stochastic processes, information theory, statistical physics and statistical inference. The different notions are illustrated with many application examples from physics and engineering science and problems with solutions allow the reader to both check his understanding and to deepen some aspects. Indeed, the main objective of Noise theory and application to physics is to be a practical guide for the reader for going from fluctuation to information. It will thus be of great interest to undergraduate or postgraduate students and researchers in physics and engineering sciences.

### What people are saying -Write a review

We haven't found any reviews in the usual places.

### Contents

 Introduction 1 Random Variables 5 21 Random Events and Probability 6 22 Random Variables 7 23 Means and Moments 10 24 Median and Mode of a Probability Distribution 12 25 Joint Random Variables 13 26 Covariance 16
 Lagrange Multipliers 133 Exercises 134 Thermodynamic Fluctuations 137 62 Free Energy 141 63 Connection with Thermodynamics 142 64 Covariance of Fluctuations 143 65 A Simple Example 146 66 FluctuationDissipation Theorem 149

 27 Change of Variables 18 28 Stochastic Vectors 19 Exercises 22 Fluctuations and Covariance 25 32 Stationarity and Ergodicity 28 33 Ergodicity in Statistical Physics 32 34 Generalization to Stochastic Fields 34 35 Random Sequences and Cyclostationarity 35 36 Ergodic and Stationary Cases 40 37 Application to Optical Coherence 41 38 Fields and Partial Differential Equations 42 39 Power Spectral Density 44 310 Filters and Fluctuations 46 311 Application to Optical Imaging 50 312 Green Functions and Fluctuations 52 313 Stochastic Vector Fields 56 314 Application to the Polarization of Light 57 315 Ergodicity and Polarization of Light 61 WienerKhinchine Theorem 64 Exercises 66 Limit Theorems and Fluctuations 71 42 Characteristic Function 74 43 Central Limit Theorem 76 44 Gaussian Noise and Stable Probability Laws 80 45 A Simple Model of Speckle 81 46 Random Walks 89 47 Application to Diffusion 92 48 Random Walks and Space Dimensions 97 49 Rare Events and Particle Noise 100 410 Low Flux Speckle 102 Exercises 104 Information and Fluctuations 109 52 Entropy 111 53 Kolmogorov Complexity 114 54 Information and Stochastic Processes 117 55 Maximum Entropy Principle 119 56 Entropy of Continuous Distributions 122 57 Entropy Propagation and Diffusion 124 58 Multidimensional Gaussian Case 128 59 KullbackLeibler Measure 130
 67 Noise at the Terminals of an RC Circuit 153 68 Phase Transitions 158 69 Critical Fluctuations 161 Exercises 163 Statistical Estimation 167 72 The Language of Statistics 169 74 Maximum Likelihood Estimator 174 75 CramerRao Bound in the Scalar Case 177 76 Exponential Family 179 77 Example Applications 181 78 CramerRao Bound in the Vectorial Case 182 79 Likelihood and the Exponential Family 183 710 Examples in the Exponential Family 186 7101 Estimating the Parameter in the Poisson Distribution 187 7103 Estimating the Mean of the Gaussian Distribution 188 7104 Estimating the Variance of the Gaussian Distribution 189 7105 Estimating the Mean of the Weibull Distribution 190 711 Robustness of Estimators 192 Scalar CramerRao Bound 196 Efficient Statistics 199 Vectorial CramerRao Bound 200 Exercises 205 Examples of Estimation in Physics 209 82 Measurement Accuracy in the Presence of Gaussian Noise 212 83 Estimating a Detection Efficiency 217 84 Estimating the Covariance Matrix 219 85 Application to Coherency Matrices 221 86 Making Estimates in the Presence of Speckle 224 87 FluctuationDissipation and Estimation 225 Exercises 227 Solutions to Exercises 231 92 Chapter Three Fluctuations and Covariance 235 93 Chapter Four Limit Theorems and Fluctuations 243 94 Chapter Five Information and Fluctuations 250 95 Chapter Six Statistical Physics 259 96 Chapter Seven Statistical Estimation 266 97 Chapter Eight Examples of Estimation in Physics 271 References 285 Index 287 Copyright

### References from web pages

Zentralblatt MATH Database 1931 – 2008 pre02199282
Noise theory and application to physics. From fluctuations to information. With a foreword by Nino Boccara. (English). Advanced Texts in Physics. ...
zmath.impa.br/ cgi-bin/ zmen/ ZMATH/ en/ quick.html?first=1& maxdocs=3& bi_op=contains& type=pdf& an=02199282& format=complete

Phys. Rev. A 77, 043606 (2008): Negretti et al. - Quantum-limited ...
Quantum-limited position measurements of a dark matter-wave soliton. Antonio Negretti1*, Carsten Henkel2, and Klaus MÃ¸lmer1; 1Lundbeck Foundation ...

ebay Express: Noise Theory and Application to Physics - [KEIN ...
ebay Express Noise Theory and Application to Physics - [KEIN PORTO
item.express.ebay.de/ Noise-Theory-and-Application-to-Physics-KEIN-PORTO_W0QQitemZ130194585445QQihZ003QQcmdZExpressItem

Scanning Electron Microscopy
Scanning Electron Microscopy Springer verlag Berlin And Heidelbe
www.agapea.com/ Scanning-Electron-Microscopy-n1222241i.htm

Mathematics
ﺎﺗ. ١۵. هﺎﻣ رذآ. ١٣٨۶. Mathematics. Book Code. Title. Year. Author. Price(Rial). Row. Publisher. List_price. A Natural Introduction to Probability Theory ...
www.modares.ac.ir/ bookfair/ Sciences.PDF