What is the relationship between large deviation and weak convergence? Consider a sequence of random variables {X_n}, does the LDP of sample mean imply the the distribution of X_n converge? If so, what is the relation between LDP rate function and weak convergence rate?
2026-03-26 03:18:58.1774495138
Connection between large deviation principle and weak convergence/
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I think the answer is NO, since large deviation tells something about the deviation of size $n$, not $\sqrt{n}$ as required in weak convergence results(like CLT).