Continuity and uniqueness of percolation critical parameters in Finitary Random Interlacements

TL;DR

This paper proves that the critical percolation parameter for Finitary Random Interlacements varies continuously with the path length parameter, establishing a key property of the phase transition in this model.

Contribution

It demonstrates the continuity of the critical percolation parameter in Finitary Random Interlacements and links it to the equality of natural critical parameters.

Findings

Critical parameter is continuous in T

Equality of natural critical parameters established

Supports phase transition analysis in FRI

Abstract

We prove that the critical percolation parameter for Finitary Random Interlacements (FRI) is continuous with respect to the path length parameter $T$. The proof uses a result which is interesting on its own right; equality of natural critical parameters for FRI percolation phase transition.