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Aldous's Poisson–Dirichlet conjecture for the random interchange model
Let $L^{(1)},L^{(2)},\dots$ denote loop lengths in decreasing order, and normalize the macroscopic loop lengths by their total length. A random partition of $[0,1]$ is obtained fro…
Conjecturesolvedpoisson-dirichlet-distributions probability random-interchange-modelarXiv posted 2 days ago
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Aldous's Poisson-Dirichlet conjecture for random interchange loops
Aldous's conjecture. This random partition has Poisson-Dirichlet $(1)$ distribution.
Conjecturesolvedpoisson-dirichlet random-interchange-model random-loopsarXiv posted 2 days ago

Aldous's Poisson–Dirichlet conjecture for the random interchange model