From the reviews: "Philippe Refregier's book is an introduction to the fundamental principles of randomness that can be encountered in a physicist's everyday life. ... Refregier's book is a good textbook for physics graduate students and researchers who want to go a little deeper into probability theory ... . I would also recommend it to mathematicians who want to get a different point of view on probability theory. Students will undoubtedly profit from a variety of exercises that come with ... solutions." (Achim Klenke, Zentralblatt MATH, Vol. 1092 (18), 2006) "The book provides a good presentation of the statistical basis for theories of noise in physics. ... Noise theory and application to physics provides a precise description of the theoretical background and practical tools for noise and fluctuation analyses. It will thus be of great interest to undergraduate or postgraduate students and researchers in physics and the engineering sciences." (Stefan Adams, Mathematical Reviews, Issue 2006 e)

• 1 Introduction.- 2 Random Variables.- 2.1 Random Events and Probability.- 2.2 Random Variables.- 2.3 Means and Moments.- 2.4 Median and Mode of a Probability Distribution.- 2.5 Joint Random Variables.- 2.6 Covariance.- 2.7 Change of Variables.- 2.8 Stochastic Vectors.- Exercises.- 3 Fluctuations and Covariance.- 3.1 Stochastic Processes.- 3.2 Stationarity and Ergodicity.- 3.3 Ergodicity in Statistical Physics.- 3.4 Generalization to Stochastic Fields.- 3.5 Random Sequences and Cyclostationarity.- 3.6 Ergodic and Stationary Cases.- 3.7 Application to Optical Coherence.- 3.8 Fields and Partial Differential Equations.- 3.9 Power Spectral Density.- 3.10 Filters and Fluctuations.- 3.11 Application to Optical Imaging.- 3.12 Green Functions and Fluctuations.- 3.13 Stochastic Vector Fields.- 3.14 Application to the Polarization of Light.- 3.15 Ergodicity and Polarization of Light.- 3.16 Appendix: Wiener–Khinchine Theorem.- Exercises.- 4 Limit Theorems and Fluctuations.- 4.1 Sum of Random Variables.- 4.2 Characteristic Function.- 4.3 Central Limit Theorem.- 4.4 Gaussian Noise and Stable Probability Laws.- 4.5 A Simple Model of Speckle.- 4.6 Random Walks.- 4.7 Application to Diffusion.- 4.8 Random Walks and Space Dimensions.- 4.9 Rare Events and Particle Noise.- 4.10 Low Flux Speckle.- Exercises.- 5 Information and Fluctuations.- 5.1 Shannon Information.- 5.2 Entropy.- 5.3 Kolmogorov Complexity.- 5.4 Information and Stochastic Processes.- 5.5 Maximum Entropy Principle.- 5.6 Entropy of Continuous Distributions.- 5.7 Entropy, Propagation and Diffusion.- 5.8 Multidimensional Gaussian Case.- 5.9 Kullback-Leibler Measure.- 5.10 Appendix: Lagrange Multipliers.- Exercises.- 6 Thermodynamic Fluctuations.- 6.1 Gibbs Statistics.- 6.2 Free Energy.- 6.3 Connection with Thermodynamics.- 6.4Covariance of Fluctuations.- 6.5 A Simple Example.- 6.6 Fluctuation-Dissipation Theorem.- 6.7 Noise at the Terminals of an RC Circuit.- 6.8 Phase Transitions.- 6.9 Critical Fluctuations.- Exercises.- 7 Statistical Estimation.- 7.1 The Example of Poisson Noise.- 7.2 The Language of Statistics.- 7.3 Characterizing an Estimator.- 7.4 Maximum Likelihood Estimator.- 7.5 Cramer-Rao Bound in the Scalar Case.- 7.6 Exponential Family.- 7.7 Example Applications.- 7.8 Cramer-Rao Bound in the Vectorial Case.- 7.9 Likelihood and the Exponential Family.- 7.10 Examples in the Exponential Family.- 7.11 Robustness of Estimators.- 7.12 Appendix: Scalar Cramer-Rao Bound.- 7.13 Appendix: Efficient Statistics.- 7.14 Appendix: Vectorial Cramer-Rao Bound.- Exercises.- 8 Examples of Estimation in Physics.- 8.1 Measurement of Optical Flux.- 8.2 Measurement Accuracy in the Presence of Gaussian Noise.- 8.3 Estimating a Detection Efficiency.- 8.4 Estimating the Covariance Matrix.- 8.5 Application to Coherency Matrices.- 8.6 Making Estimates in the Presence of Speckle.- 8.7 Fluctuation-Dissipation and Estimation.- Exercises.- 9 Solutions to Exercises.- 9.1 Chapter Two. Random Variables.- 9.2 Chapter Three. Fluctuations and Covariance.- 9.3 Chapter Four. Limit Theorems and Fluctuations.- 9.4 Chapter Five. Information and Fluctuations.- 9.5 Chapter Six. Statistical Physics.- 9.6 Chapter Seven. Statistical Estimation.- 9.7 Chapter Eight. Examples of Estimation in Physics.- References.

From the reviews: "Philippe Refregier's book is an introduction to the fundamental principles of randomness that can be encountered in a physicist's everyday life. ... Refregier's book is a good textbook for physics graduate students and researchers who want to go a little deeper into probability theory ... . I would also recommend it to mathematicians who want to get a different point of view on probability theory. Students will undoubtedly profit from a variety of exercises that come with ... solutions." (Achim Klenke, Zentralblatt MATH, Vol. 1092 (18), 2006) "The book provides a good presentation of the statistical basis for theories of noise in physics. ... Noise theory and application to physics provides a precise description of the theoretical background and practical tools for noise and fluctuation analyses. It will thus be of great interest to undergraduate or postgraduate students and researchers in physics and the engineering sciences." (Stefan Adams, Mathematical Reviews, Issue 2006 e)

• 1 Introduction.- 2 Random Variables.- 2.1 Random Events and Probability.- 2.2 Random Variables.- 2.3 Means and Moments.- 2.4 Median and Mode of a Probability Distribution.- 2.5 Joint Random Variables.- 2.6 Covariance.- 2.7 Change of Variables.- 2.8 Stochastic Vectors.- Exercises.- 3 Fluctuations and Covariance.- 3.1 Stochastic Processes.- 3.2 Stationarity and Ergodicity.- 3.3 Ergodicity in Statistical Physics.- 3.4 Generalization to Stochastic Fields.- 3.5 Random Sequences and Cyclostationarity.- 3.6 Ergodic and Stationary Cases.- 3.7 Application to Optical Coherence.- 3.8 Fields and Partial Differential Equations.- 3.9 Power Spectral Density.- 3.10 Filters and Fluctuations.- 3.11 Application to Optical Imaging.- 3.12 Green Functions and Fluctuations.- 3.13 Stochastic Vector Fields.- 3.14 Application to the Polarization of Light.- 3.15 Ergodicity and Polarization of Light.- 3.16 Appendix: Wiener–Khinchine Theorem.- Exercises.- 4 Limit Theorems and Fluctuations.- 4.1 Sum of Random Variables.- 4.2 Characteristic Function.- 4.3 Central Limit Theorem.- 4.4 Gaussian Noise and Stable Probability Laws.- 4.5 A Simple Model of Speckle.- 4.6 Random Walks.- 4.7 Application to Diffusion.- 4.8 Random Walks and Space Dimensions.- 4.9 Rare Events and Particle Noise.- 4.10 Low Flux Speckle.- Exercises.- 5 Information and Fluctuations.- 5.1 Shannon Information.- 5.2 Entropy.- 5.3 Kolmogorov Complexity.- 5.4 Information and Stochastic Processes.- 5.5 Maximum Entropy Principle.- 5.6 Entropy of Continuous Distributions.- 5.7 Entropy, Propagation and Diffusion.- 5.8 Multidimensional Gaussian Case.- 5.9 Kullback-Leibler Measure.- 5.10 Appendix: Lagrange Multipliers.- Exercises.- 6 Thermodynamic Fluctuations.- 6.1 Gibbs Statistics.- 6.2 Free Energy.- 6.3 Connection with Thermodynamics.- 6.4Covariance of Fluctuations.- 6.5 A Simple Example.- 6.6 Fluctuation-Dissipation Theorem.- 6.7 Noise at the Terminals of an RC Circuit.- 6.8 Phase Transitions.- 6.9 Critical Fluctuations.- Exercises.- 7 Statistical Estimation.- 7.1 The Example of Poisson Noise.- 7.2 The Language of Statistics.- 7.3 Characterizing an Estimator.- 7.4 Maximum Likelihood Estimator.- 7.5 Cramer-Rao Bound in the Scalar Case.- 7.6 Exponential Family.- 7.7 Example Applications.- 7.8 Cramer-Rao Bound in the Vectorial Case.- 7.9 Likelihood and the Exponential Family.- 7.10 Examples in the Exponential Family.- 7.11 Robustness of Estimators.- 7.12 Appendix: Scalar Cramer-Rao Bound.- 7.13 Appendix: Efficient Statistics.- 7.14 Appendix: Vectorial Cramer-Rao Bound.- Exercises.- 8 Examples of Estimation in Physics.- 8.1 Measurement of Optical Flux.- 8.2 Measurement Accuracy in the Presence of Gaussian Noise.- 8.3 Estimating a Detection Efficiency.- 8.4 Estimating the Covariance Matrix.- 8.5 Application to Coherency Matrices.- 8.6 Making Estimates in the Presence of Speckle.- 8.7 Fluctuation-Dissipation and Estimation.- Exercises.- 9 Solutions to Exercises.- 9.1 Chapter Two. Random Variables.- 9.2 Chapter Three. Fluctuations and Covariance.- 9.3 Chapter Four. Limit Theorems and Fluctuations.- 9.4 Chapter Five. Information and Fluctuations.- 9.5 Chapter Six. Statistical Physics.- 9.6 Chapter Seven. Statistical Estimation.- 9.7 Chapter Eight. Examples of Estimation in Physics.- References.