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Very roughly, universality is the idea that random systems "behave the same" in large time or large-scale limits. Many of us will be familiar with this concept through the Central Limit Theorem.
In this video Andrew attempts to explain this phenomenon through examples taken from a wide area of mathematical and physical problems.
Andrews covers examples from random matrix theory, combinatorics, random growth models, and number theory. He also covers more exotic problems, such as the bus traffic in Mexico and "Guendy the Snake".