Noise Theory and Application to Physics: From Fluctuations to Information

I had great pleasure in reading Philippe Refregier's book on the theory of noise and its applications in physics. The main aim of the book is to present the basic ideas used to characterize these unwanted random signals that obscure information content. To this end, the author devotes a sigificant part of his book to a detailed study of the probabilistic foundations of fluctuation theory. Following a concise and accurate account of the basics of probability the­ ory, the author includes a detailed study of stochastic processes, emphasizing the idea of the correlation function, which plays a key role in many areas of physics. Physicists often assume that the noise perturbing a signal is Gaussian. This hypothesis is justified if one can consider that the noise results from the superposition of a great many independent random perturbations. It is this fact that brings the author to discuss the theory underlying the addition of random variables, accompanied by a wide range of illustrative examples. Since noise affects information, the author is naturally led to consider Shannon's information theory, which in turn brings him to the altogether fundamental idea of entropy. This chapter is completed with a study of com­ plexity according to Kolmogorov. This idea is not commonly discussed in physics and the reader will certainly appreciate the clear presentation within these pages.