Spectral dimensions for one-dimensional critical long-range percolation
Abstract
Consider critical long-range percolation on ℤ, where an edge connects i and j independently with probability 1−exp{−β∫ii+1∫jj+1|u−v|−2dudv} for |i−j|>1 for some fixed β>0 and with probability 1 for |i−j|=1. We prove that both the quenched and annealed spectral dimensions of the associated simple random walk are 2∕(1+δ), where δ∈(0,1) (depending only on β) is the exponent of the effective resistance in this model, as derived in [10, Theorem 1.1]. Our work addresses an open question from [7, Section 5].
Fields of Study & Subjects
Stochastic processes and statistical mechanics
Mathematical Dynamics and Fractals
Theoretical and Computational Physics
Publication details
- Journal / source
- Electronic Journal of Probability
- Volume
- 31
- Issue
- none
- Pages
- 1–15
- Publication date
- 1 January 2026
- Language
- EN