Exponential Localization of Spatial Random Permutations in One Dimension
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 W3, 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 W2.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.