Lower heavy-tail conjecture for the nearest-interferer path-loss ratio

Let $x_0$ be the desired transmitter and $y$ the nearest interferer. Let $\theta$ denote the SIR threshold, $\theta\to0$, let $P_{\rm s}(\theta)$ be the success probability, and let $\delta$ be the path-loss parameter. The ratio $\ell(x_0)/\ell(y)$ compares the mean desired and nearest-interferer powers.

Lower heavy-tail conjecture.

$$0\in\operatorname{supp}(\ell(x_0)/\ell(y)) \quad \Longleftrightarrow \quad 1-P_{\rm s}(\theta)=\Theta(\theta^{\delta}),\quad\theta\to0.$$

This conjecture says that an arbitrarily large mean nearest-interferer power relative to the desired power is equivalent to lower-tail outage decay of order $\theta^{\delta}$. The source presents this as a conjectural generalization of its asymptotic results for cellular and ad hoc network models; its resolution is not specified.