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arXiv · 2603.01242

Exponential Localization of Spatial Random Permutations in One Dimension

Reuben Drogin·Felipe Hernández
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Abstract

We consider a class of random permutations of the interval $[-n,n]$, in which points are typically displaced a distance $O(W)$. We show the cycles are localized on the scale $W^3$, with an exponentially decaying tail bound. Analogous to eigenfunctions of one dimensional random band matrices, the cycles are conjectured to be localized to the scale $W^2.$

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Reuben Drogin, Felipe Hernández. 2026-03-01. Exponential Localization of Spatial Random Permutations in One Dimension. https://arxiv.org/abs/2603.01242

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