How does Random Forest relate to asymptotic normality of ensemble predictors?

Under certain assumptions, Random Forest predictions can converge to a normal distribution due to averaging many weakly dependent trees.

Each tree in a Random Forest can be viewed as a random variable T_i(x). The ensemble prediction is an average: f̂(x) = (1/T) Σ T_i(x). When trees are sufficiently decorrelated via bootstrapping and feature subsampling, the Lindeberg–Feller Central Limit Theorem applies approximately. This yields asymptotic normality of predictions around the true conditional expectation E[Y|X=x], enabling confidence interval construction in theoretical settings.