Noise in physics is related to a variety of domains, such as information theory, statistical physics, probability, stochastic processes and statistics. Noise Theory and Application to Physics provides a general background on noise theory, along with techniques to describe and extract information in the presence of fluctuations, with the goal of featuring noise in the context of its connection with other domains. Readers will gain a deep understanding of noise theory, while acquiring systematic techniques for describing and extracting noise data.

Includes supplementary material: sn.pub/extras

Autorentext
Noise in physics is related to a variety of domains, such as information theory, statistical physics, probability, stochastic processes and statistics. Noise Theory and Application to Physics provides a general background on noise theory, along with techniques to describe and extract information in the presence of fluctuations, with the goal of featuring noise in the context of its connection with other domains. Readers will gain a deep understanding of noise theory, while acquiring systematic techniques for describing and extracting noise data.

Inhalt
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: WienerKhinchine 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.