Central limit theorem for the random assignment problem

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This event attributed to Gilles Mordant

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Claims the central limit theorem for the bipartite random assignment problem with bounded uniform costs: $\sqrt{n}\,(C_n-\zeta(2)) \Rightarrow \mathcal{N}(0,\,4\zeta(2)-4\zeta(3))$. The limiting constant is not itself new - Wästlund had computed exactly $4\zeta(2)-4\zeta(3)$ for the mean-one exponential model, and Malatesta, Parisi and Sicuro derived the non-bipartite analogue by replicas - but neither is a proof for the bounded bipartite model, and Wästlund's zero-free-disk conjecture, which would imply a Gaussian limit, remains open. So the value was expected; the proof of convergence to it is what is claimed. The route is an exact change of variables on an optimal dual potential, after which the residual dependence is a single directed-tree factor whose matrix-tree determinant becomes triangular once the potentials are ordered. parent of this event

VibeMathed record: Central limit theorem for the random assignment problem evidence for this event

Central limit theorem for the random assignment problem evidence for this event

Central limit theorem for the random assignment problem parent of this event

Aldous, The zeta(2) limit in the random assignment problem evidence for this event