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Explore the fascinating connections between random matrix theory and diverse mathematical phenomena through this 28-minute conference talk from JuliaCon Local Paris 2025. Discover how seemingly unrelated concepts like corner growth, random domino tilings, nonintersecting paths, and Young tableaux generated from random words can all be unified through determinantal point processes. Learn about specialized Julia packages designed for statistical analysis of these mathematical structures, with particular emphasis on interactive exploration capabilities using modern tools like Pluto.jl and WGLMakie.jl. Gain insights into practical implementations that make complex random matrix theory concepts accessible through interactive computational environments, demonstrating Julia's powerful capabilities for mathematical research and visualization.
