Convergence Rates for the $p$-Wasserstein Distance of the Empirical Measures of an Ergodic Markov Process
Published:Dec 28, 2025 14:02
•1 min read
•ArXiv
Analysis
This article likely presents mathematical analysis and proofs related to the convergence properties of empirical measures derived from ergodic Markov processes, specifically focusing on the $p$-Wasserstein distance. The research likely explores how quickly these empirical measures converge to the true distribution as the number of samples increases. The use of the term "ergodic" suggests the Markov process has a long-term stationary distribution. The $p$-Wasserstein distance is a metric used to measure the distance between probability distributions.
Key Takeaways
- •Focuses on the convergence of empirical measures derived from ergodic Markov processes.
- •Uses the $p$-Wasserstein distance to quantify the distance between distributions.
- •Likely provides theoretical results on convergence rates.
- •Relevant to fields like machine learning and statistics where analyzing the convergence of empirical distributions is important.
Reference
“The title suggests a focus on theoretical analysis within the field of probability and statistics, specifically related to Markov processes and the Wasserstein distance.”