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Article summary:
1. The article discusses limit theorems in Wasserstein distance for empirical measures of diffusion processes on Riemannian manifolds.
2. It establishes a finite limit when the dimension is less than or equal to 3, and provides estimates for the limit when the dimension is greater than or equal to 5.
3. The article also establishes a long-time large deviation principle with a good rate function given by the information with respect to μ.
Article analysis:
The article appears to be well-researched and reliable, as it provides detailed mathematical proofs and explanations for its claims. The authors have provided sufficient evidence to support their claims, such as providing estimates for the limit when the dimension is greater than or equal to 5, and establishing a long-time large deviation principle with a good rate function given by the information with respect to μ. Furthermore, they have acknowledged potential sources of bias in their research, such as noting that their results may not hold if ∂M≠∅ (i.e., if there is a boundary).
The article does not appear to be biased or one-sided in any way; rather, it presents both sides of an argument equally and objectively. Additionally, all claims are supported by evidence from other sources (such as citing relevant literature), which adds further credibility to the article's findings. Finally, no promotional content was found in this article; rather, it focuses solely on presenting its findings in an unbiased manner.