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This lecture from the Harvard CMSA program on Classical, quantum, and probabilistic integrable systems explores random partitions at high temperature. Join speaker Cesar Cuenca from Ohio State University as he examines discrete particle ensembles x₁>x₂>...>xₙ with inverse temperature beta approaching zero while the number of particles approaches infinity. Learn about Fourier transforms based on Jack symmetric polynomials, discover the Law of Large Numbers proof, and understand how the limiting measure is characterized through a moment problem. Explore how fixed-time distributions of special Markov chains can be expressed using eigenvalues of Jacobi operators. This presentation is part of the novel interactions and applications series held on May 9, 2025.
