Foundations of Continuum Percolation and the Boolean Model

Spatial randomness and connectivity play a central role in modeling wireless networks, material science, and physical systems. This course introduces you to the core mathematics and intuitions behind the Boolean model and continuum percolation without unnecessary complexity. You will build a structured understanding of how random collections of shapes interact in space and when large-scale connectivity emerges. What you'll learn: - Understand the fundamental properties of homogeneous Poisson point processes - Define the Boolean model and analyze random spatial coverage in Euclidean space - Explore phase transitions and critical thresholds in continuum percolation - Analyze the emergence and uniqueness of unbounded connected components - Examine the geometry of covered and vacant regions in random media - Connect percolation theory to modern applications in network connectivity and spatial modeling The course begins with foundational probability terminology and point process basics before guiding you through percolation mechanics, limit theorems, and structural analysis. Designed for beginners in stochastic geometry and spatial probability who want a clear, step-by-step written guide. Start reading today to master the foundations of random spatial models.