Percolation

This book, first published in 2006, explores percolation theory, presenting classical results for non-specialists and detailing Smirnov's findings on conformal invariance, with clear proofs and illustrative examples.

Percolation, first published in 2006, serves as a comprehensive introduction to percolation theory, a mathematical framework that has evolved over the past fifty years to study random physical processes, particularly those involving flow through disordered porous media. The book aims to make classical results accessible to non-specialists while also highlighting significant contributions by Smirnov in the field of conformal invariance. This dual focus makes it a valuable resource for a diverse audience, including mathematicians, physicists, electrical engineers, and computer scientists.

The authors present the content in a streamlined manner, ensuring that the proofs are elegant and straightforward, requiring only a minimal background in probability and graph theory. This approach allows readers from various disciplines to engage with the material without feeling overwhelmed. Numerous examples are included to illustrate key concepts, enhancing the reader's understanding and providing practical applications of the theory.

Furthermore, the book outlines the proof that the critical probability for random Voronoi percolation in the plane is 1/2, a significant result in the field. By combining theoretical insights with practical examples, Percolation not only enriches the reader's knowledge but also encourages further exploration of this fascinating area of study. Overall, it stands as an essential reference for anyone interested in the intricacies of percolation theory and its wide-ranging implications.