This paper provides an in-depth analysis of the random forests model proposed by Leo Breiman in the 2000s. Random forests are ensemble learning methods that use multiple decision trees to make predictions. Despite their popularity and practical success, there has been limited exploration of their statistical properties. The authors focus on a simplified model suggested by Breiman, which is closer to the original algorithm but still captures its key features. They demonstrate that this model is consistent and adapts to sparsity, meaning its convergence rate depends only on the number of strong features and not on the presence of noise variables. The paper includes theoretical results showing that the variance and bias of the random forests estimate are controlled by appropriate choices of probability sequences, leading to a convergence rate that is optimal in high-dimensional settings. The authors also discuss a practical randomization mechanism to induce these probability sequences and present simulation results to illustrate the theoretical findings.This paper provides an in-depth analysis of the random forests model proposed by Leo Breiman in the 2000s. Random forests are ensemble learning methods that use multiple decision trees to make predictions. Despite their popularity and practical success, there has been limited exploration of their statistical properties. The authors focus on a simplified model suggested by Breiman, which is closer to the original algorithm but still captures its key features. They demonstrate that this model is consistent and adapts to sparsity, meaning its convergence rate depends only on the number of strong features and not on the presence of noise variables. The paper includes theoretical results showing that the variance and bias of the random forests estimate are controlled by appropriate choices of probability sequences, leading to a convergence rate that is optimal in high-dimensional settings. The authors also discuss a practical randomization mechanism to induce these probability sequences and present simulation results to illustrate the theoretical findings.