The quenched critical point for self-avoiding walk on random conductors

TL;DR

This paper establishes that the quenched critical point for self-avoiding walks on random conductors in any dimension is almost surely a constant, providing bounds that are valid universally.

Contribution

It proves the almost sure constancy of the quenched critical point and offers universal bounds applicable across all dimensions.

Findings

Quenched critical point is almost surely a constant.

Provided universal upper and lower bounds for the critical point.

Results extend previous analysis to all dimensions.

Abstract

Following similar analysis to that in Lacoin (PTRF 159, 777-808, 2014), we can show that the quenched critical point for self-avoiding walk on random conductors on the d-dimensional integer lattice is almost surely a constant, which does not depend on the location of the reference point. We provide its upper and lower bounds that are valid for all dimensions.