Table 1.

The table summarizes the propensity to resetting in terms of the decay of $p_n:=Pr({\mathbf{t}}_1=n)$ and the equilibrium distribution. In all cases $\lambda >0$.

${\mathit{p}}_{\mathit{n}\to \mathit{\infty }}$	${\mathit{F}}_{{\mathbf{t}}_1}\left(\mathit{n}\right)$	${\mathit{q}}_{\mathit{n}\to \mathit{\infty }}$	Propensity	Tails	$\mathbb{E}{\mathbf{t}}_1$	${\mathit{\pi }}_{\mathit{n}\to \mathit{\infty }}$
$O\left(e^{-\lambda n^{\alpha }}\right),\alpha >1$	$O(e^{-\lambda n^{\alpha }})$	0	$\mathrm{inclined}$	Super-exp.	<∞	$O\left(e^{-\lambda n^{\alpha }}\right)$
$O({(\frac{e^{-\lambda }}{n})}^n,$	$O({(\frac{e^{-\lambda }}{n})}^n,$	0	$\mathrm{inclined}$	Super-exp.	<∞	$O({(\frac{e^{-\lambda }}{n})}^n$
$O\left(e^{-\lambda n}\right)$	$O\left(e^{-\lambda n}\right)$	$\in (0,1)$	$\mathrm{neutral}$	$\exp .$	<∞	$O\left(e^{-\lambda n}\right)$
$O\left(e^{-\lambda n^{\alpha }}\right),0<\alpha <1$	$O\left(e^{-\lambda n^{\alpha }}\right),0<\alpha <1$	1	$\mathrm{averse}$	Sub-exp.	<∞	$O\left(e^{-\lambda n^{\alpha }}\right)$
$O(1/n^{\alpha }),\alpha >2$	$O(1/n^{\alpha -1}),\alpha >2$	1	$\mathrm{averse}$	Power-law	<∞	$O\left(n^{1-\alpha }\right)$
$O(1/n^{\alpha }),1<\alpha \le 2$	$O(1/n^{\alpha -1}),1<\alpha \le 2$	1	$\mathrm{averse}$	Power-law	=∞	—-