In summary, "Brownian Motions and Quantifying Randomness in Physical Systems" explores the concept of Brownian motion as a fundamental model for understanding randomness in physical processes. It discusses how this stochastic phenomenon arises from the random movement of particles suspended in a fluid, influenced by thermal fluctuations. The paper emphasizes the mathematical frameworks used to quantify randomness, including statistical mechanics and probability theory, and highlights the implications of these concepts in various scientific fields, such as physics, finance, and biological systems. Overall, it underscores the importance of Brownian motion in modeling and predicting the behavior of complex systems characterized by uncertainty.
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Stochastic calculus has come a long way since Robert Brown described the motion of pollen through a microscope in 1827. It’s now a key player in data science, quant finance, and mathematical biology. This article is drawn from notes I wrote for an undergraduate statistical physics course a few months ago. There won’t be any mathematical rigor.
