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Explore a comprehensive lecture on the polynuclear growth model (PNG) presented by Daniel Remenik from the Universidad de Chile at IPAM's Vertex Models workshop. Delve into the intricacies of this one-dimensional crystal growth model, a fundamental component of the KPZ universality class. Discover how the PNG model in droplet geometry relates to the longest increasing subsequence problem for random permutations. Examine a proof of the Fredholm determinant formula for multipoint distributions of PNG with arbitrary initial data, based on probabilistic arguments, invariant measure, and time reversal symmetry. Uncover the connection between this formula and the 2D Toda lattice, gaining valuable insights into the algebraic and probabilistic aspects of universality in vertex models.
