Scaling limit of the occupation measure of random walk cut points
Abstract
We consider the occupation measure of the cut points of a simple random walk on a d-dimensional cubic lattice for d=2,3, and show that the scaling limit of the occupation measure is the natural fractal measure on the Brownian cut points defined via its Minkowski content. Moreover, we also establish the convergence of the n-point cut point Green’s function towards its continuum counterpart, which is conformally covariant.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Stochastic processes and statistical mechanics
Theoretical and Computational Physics
Publication details
- Journal / source
- Electronic Journal of Probability
- Volume
- 31
- Issue
- none
- Publication date
- 1 January 2026
- Language
- EN