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 $W^3$, 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 $W^2.$
Fields of Study & Subjects
Random Matrices and Applications
Spectral Theory in Mathematical Physics
Stochastic processes and statistical mechanics
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 1 March 2026
- Language
- EN
- Document type
- Preprint