Reuben Drogin

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math.PR2026

Exponential Localization of Spatial Random Permutations in One Dimension

Reuben Drogin, Felipe HernÃ¡ndez

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 $W^{3}$ ,…

math.PR2026

Local limit theorems for random isometries of the plane

Reuben Drogin, Felipe HernÃ¡ndez

We consider a random walk $(Y_{N})_{N \geq 0}$ on $R^{2}$ generated by successively applying independent random isometries, drawn from a fixed measure $I^¼$ , to the point $0$ . W…

math.PR2025

The regular tree Anderson model at low disorder

Reuben Drogin, Charles K Smart

We prove delocalization for the Anderson model on an infinite regular tree (or Cayley graph or Bethe lattice) at low disorder. This extends earlier results of Klein and Aizenman--W…

math.PR2025

Localization of One-Dimensional Random Band Matrices

Reuben Drogin

We consider a general class of $n \times n$ random band matrices with bandwidth $W$ . When $W^{2} ≪ n$ , we prove that with high probability the eigenvectors of such matrices are local…

math.PR2025

Long range voter models and dynamical fractional Brownian motion

Reuben Drogin

We study the voter model on Z with long-range interactions, as proposed by Hammond and Sheffield. We show a spacetime rescaling converges to a fractional Gaussian free field, which…