The book explores isotropic random sections of fiber bundles through a multidisciplinary lens, integrating mathematics and physics. It focuses on developing rigorous mathematical models for both observed and theoretical cosmic backgrounds, offering insights into the probabilistic frameworks that underpin our understanding of the universe's foundational structures.
The author describes the current state of the art in the theory of invariant random fields. This theory is based on several different areas of mathematics, including probability theory, differential geometry, harmonic analysis, and special functions. The present volume unifies many results scattered throughout the mathematical, physical, and engineering literature, as well as it introduces new results from this area first proved by the author. The book also presents many practical applications, in particular in such highly interesting areas as approximation theory, cosmology and earthquake engineering. It is intended for researchers and specialists working in the fields of stochastic processes, statistics, functional analysis, astronomy, and engineering.