forest on ${\mathbb{Z}}^d$ whose scaling limit is $\operatorname{FGF}_2({\mathbb{R}}^d)$ [@sun2013uniform].

Fractional Gaussian fields in one dimension
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The $\operatorname{FGF}_s({\mathbb{R}}^d)$ processes are easiest to classify and explain when $d=1$. We first consider ${H}= s-\frac{d}{2} \in (0,1)$ (so that $s \in
(1/2, 3/2)$), in which case the $\operatorname{FGF}_s({\mathbb{R}})$ is a Gaussian random function $h: {\mathbb{R}}\to {\mathbb{R}}$ which we interpret as being defined modulo an additive constant. This means that while the quantity $h(t)$ is not a well-defined random variable for $t \in {\mathbb{R}}$, the quantity $h(t_1) - h(t_2)$ is a well-defined random variable for $t_1,t_2 \in {\mathbb{R}}$. When $H\in (0,1)$, the $\operatorname{FGF}_s({\mathbb{R}})$ is the stationary-increment form of the [**fractional Brownian motion with Hurst parameter ${H}$**]{}. The law of the fractional Brownian motion is determined by the variance formula $$\operatorname{Var}\bigl(h(t_1) - h(t_2)\bigr) =
|t_1 - t_2|^{H}.$$ When ${H}= 0$, so that $s=1/2$, the $\operatorname{FGF}_s({\mathbb{R}})$ is the log-correlated Gaussian field (LGF), which is defined as a random tempered distribution modulo additive constant.

When $d=1$ the weak derivative of an $\operatorname{FGF}_s({\mathbb{R}})$ is an $\operatorname{FGF}_{s-1}({\mathbb{R}})$. Thus all $\operatorname{FGF}_s({\mathbb{R}})$ processes may be obtained by either integrating or differentiating fractional Brownian motion (with $s \in (1/2, 3/2)$) or the LGF ($s=1/2$) an integral number of times. From this, it 