The paper titled "Differential privacy guarantees of Markov chain Monte Carlo algorithms," published on November 4, 2025, addresses the challenge of ensuring differential privacy within Markov chain Monte Carlo (MCMC) methods. It emphasizes the critical role that convergence properties play in achieving these privacy guarantees, suggesting that understanding how MCMC algorithms converge is essential for maintaining data privacy. By focusing on these convergence aspects, the paper provides valuable insights that can aid researchers working on privacy-preserving algorithms in machine learning and statistics. This contribution is particularly relevant as differential privacy becomes increasingly important in safeguarding sensitive information during data analysis. The study thus advances the theoretical framework for integrating privacy guarantees into widely used computational techniques like MCMC. Overall, the work highlights a nuanced approach to balancing algorithmic performance with privacy requirements.