At the present moment, after the success of the renormalization group in providing a conceptual framework for studying second-order phase tran­ sitions, we have a nearly satisfactory understanding of the statistical me­ chanics of classical systems with a non-random Hamiltonian. The situation is completely different if we consider the theory of systems with a random Hamiltonian or of chaotic dynamical systems. The two fields are connected; in fact, in the latter the effects of deterministic chaos can be modelled by an appropriate stochastic process. Although many interesting results have been obtained in recent years and much progress has been made, we still lack a satisfactory understanding of the extremely wide variety of phenomena which are present in these fields. The study of disordered or chaotic systems is the new frontier where new ideas and techniques are being developed. More interesting and deep results are expected to come in future years. The properties of random matrices and their products form a basic tool, whose importance cannot be underestimated. They playa role as important as Fourier transforms for differential equations. This book is extremely interesting as far as it presents a unified approach for the main results which have been obtained in the study of random ma­ trices. It will become a reference book for people working in the subject. The book is written by physicists, uses the language of physics and I am sure that many physicists will read it with great pleasure.

As MOS devices are scaled to meet increasingly demanding circuit specifications, process variations have a greater effect on the reliability of circuit performance. For this reason, statistical techniques are required to design integrated circuits with maximum yield. Statistical Modeling for Computer-Aided Design of MOS VLSI Circuits describes a statistical circuit simulation and optimization environment for VLSI circuit designers. The first step toward accomplishing statistical circuit design and optimization is the development of an accurate CAD tool capable of performing statistical simulation. This tool must be based on a statistical model which comprehends the effect of device and circuit characteristics, such as device size, bias, and circuit layout, which are under the control of the circuit designer on the variability of circuit performance. The distinctive feature of the CAD tool described in this book is its ability to accurately model and simulate the effect in both intra- and inter-die process variability on analog/digital circuits, accounting for the effects of the aforementioned device and circuit characteristics. Statistical Modeling for Computer-Aided Design of MOS VLSI Circuits serves as an excellent reference for those working in the field, and may be used as the text for an advanced course on the subject.

consequences of broken symmetry -here parity-is studied. In this model, turbulence is dominated by a hierarchy of helical (corkscrew) structures. The authors stress the unique features of such pseudo-scalar cascades as well as the extreme nature of the resulting (intermittent) fluctuations. Intermittent turbulent cascades was also the theme of a paper by us in which we show that universality classes exist for continuous cascades (in which an infinite number of cascade steps occur over a finite range of scales). This result is the multiplicative analogue of the familiar central limit theorem for the addition of random variables. Finally, an interesting paper by Pasmanter investigates the scaling associated with anomolous diffusion in a chaotic tidal basin model involving a small number of degrees of freedom. Although the statistical literature is replete with techniques for dealing with those random processes characterized by both exponentially decaying (non-scaling) autocorrelations and exponentially decaying probability distributions, there is a real paucity of literature appropriate for geophysical fields exhibiting either scaling over wide ranges (e. g. algebraic autocorrelations) or extreme fluctuations (e. g. algebraic probabilities, divergence of high order statistical moments). In fact, about the only relevant technique that is regularly used -fourier analysis (energy spectra) -permits only an estimate of a single (power law) exponent. If the fields were mono-fractal (characterized by a single fractal dimension) this would be sufficient, however their generally multifractal character calls for the development of new techniques.