The main purpose of this work is to present the appearance of universal limit probability laws in physics and their connection with the recently developed scaling theory of fluctuations. Arising from the probability theory and renormalization group methods, this approach has been proved to provide efficient investigative tools for the collective features that occur in any finite system. The mathematical background is self-contained and is formulated in terms which are easy to apply to the physical context. After illustrating the problem of anomalous diffusion, the book reviews recent advances...

The main purpose of this work is to present the appearance of universal limit probability laws in physics and their connection with the recently developed scaling theory of fluctuations. Arising from the probability theory and renormalization group methods, this approach has been proved to provide efficient investigative tools for the collective features that occur in any finite system. The mathematical background is self-contained and is formulated in terms which are easy to apply to the physical context. After illustrating the problem of anomalous diffusion, the book reviews recent advances...