1+O(1) asymptotics for loop percolation in five and higher dimensions

TL;DR

This paper derives first-order asymptotic estimates for the one-arm probability and two-point function in loop percolation models in five or more dimensions, addressing a question from prior research.

Contribution

It provides the first-order asymptotic calculations for loop percolation in high dimensions, extending understanding of critical phenomena in these models.

Findings

Calculated one-arm probability in high dimensions

Derived two-point function asymptotics

Answered a previously open question

Abstract

We calculate the one-arm probability and the two-point function for loop percolation in dimensions five and higher on the lattice up to first order. This answers a question posed by Y. Chang and A. Sapozhnikov in Probability Theory and Related Fields (2016).