The Surprising Mathematics of Longest Increasing Subsequences

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The directed landscape (2018, background): “ve been studied previously. This is a very partial review of the literature, with results most directly related to the present work. For a gentle introduction suitable for a newcomer to the area, see Romik (2015). Review articles and books focusing on more recent developments include Corwin 8 (2016)”
Efficient quantum tomography (2015, unknown): “he well known fact that Eλ1 ≤ 2 √ n when λ has the Plancherel distribution. Indeed, our proof of Theorem 5.2 extends the original proof of this fact by Vershik and Kerov [VK85] (cf. the exposition in [Rom14]). Proof. Consider the Schur–Weyl growth process under the uniform distribution (1/d,...,1/d)”
Isotonic regression in general dimensions (2017, background): “See Romik (2014) and references therein.”