Exact samplers for permutations with fixed LIS length k: O(n log log n) expected time rejection sampler when k=Theta(n), and tilde O(n^3 k^4) RS-based sampler for arbitrary k via determinant oracles on Hankel moment matrices.
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Under multicritical conditions the edge scaling limit of correlations for the shifted Schur measure converges to the higher-order Airy kernel determinant, demonstrating a Pfaffian-to-determinantal transition.
The symmetric Dyson exclusion process exhibits ballistic scaling and non-local hydrodynamics with current j[ρ] = (1/π) sin(πρ) sinh(π H ρ) where H is the Hilbert transform, equivalent to a local two-field system, with exact solutions for block initial states matching simulations.
Disappear-Sort on random sequences has expected passes equal to the expected first-column length of a Plancherel Young diagram, hence asymptotically 2√n with Tracy-Widom fluctuations.
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Exact Sampling of Permutations with a Fixed Longest Increasing Subsequence
Exact samplers for permutations with fixed LIS length k: O(n log log n) expected time rejection sampler when k=Theta(n), and tilde O(n^3 k^4) RS-based sampler for arbitrary k via determinant oracles on Hankel moment matrices.
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Multicritical Scaling Limit of Shifted Schur Measure
Under multicritical conditions the edge scaling limit of correlations for the shifted Schur measure converges to the higher-order Airy kernel determinant, demonstrating a Pfaffian-to-determinantal transition.
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Recursive Record Filtering and Longest Decreasing Subsequences
Disappear-Sort on random sequences has expected passes equal to the expected first-column length of a Plancherel Young diagram, hence asymptotically 2√n with Tracy-Widom fluctuations.