Self-Avoiding Walks and Loop-Erased Random Walk Fundamentals

Understanding non-intersecting random paths is essential for modern probability theory, statistical physics, and discrete mathematics. This text-based course guides you step-by-step through the core concepts of simple random walks, self-avoiding walks (SAW), and loop-erased random walks (LERW). You will gain a clear foundational grasp of how spatial dimensionality affects path intersections and critical behavior without complex mathematical friction. What you'll learn: Understand fundamental probability concepts, lattice paths, and basic random walk properties. Explore the definition, combinatorial growth, and spatial scaling of self-avoiding walks. Learn the construction and unique topological features of loop-erased random walks. Examine random walk intersection probabilities across different spatial dimensions. Practice analyzing modern path simulation algorithms through structured pseudocode and conceptual examples. The course begins with essential terminology and foundational definitions before advancing through rigorous yet accessible theoretical insights and comparative analysis. This course is designed for curious beginners, students of mathematics or computer science, and anyone interested in stochastic processes with no advanced background required. Start reading today to deepen your understanding of modern probabilistic models.