Random Walk Theory in Physics and Biology - Class 3

Explore the fundamental principles of random walk theory and its applications across physics and biological systems in this third lecture from the Journeys into Theoretical Physics program. Delve into the mathematical foundations of stochastic processes and discover how random walk models explain phenomena ranging from particle diffusion in physical systems to animal foraging patterns and population dynamics in biology. Learn about the statistical properties of random walks, including mean displacement, variance, and probability distributions, while examining real-world examples that demonstrate the universality of these concepts. Investigate advanced topics such as biased random walks, correlated random walks, and their role in understanding complex biological behaviors like cell migration, ecological dispersal, and evolutionary processes. Gain insights into how random walk theory bridges the gap between microscopic randomness and macroscopic patterns observed in nature, providing a powerful framework for modeling and predicting system behavior across multiple scales in both physical and biological contexts.