# Cramér’s Theorem is Atypical

@article{Gantert2016CramrsTI,
title={Cram{\'e}r’s Theorem is Atypical},
author={N. Gantert and S. S. Kim and K. Ramanan},
journal={arXiv: Probability},
year={2016},
pages={253-270}
}
• Published 2016
• Mathematics
• arXiv: Probability
• The empirical mean of n independent and identically distributed (i.i.d.) random variables $$(X_1,\dots ,X_n)$$ can be viewed as a suitably normalized scalar projection of the n-dimensional random vector $$X^{(n)}\displaystyle \mathop {=}^{\cdot }\,(X_1,\dots ,X_n)$$ in the direction of the unit vector $$n^{-1/2}(1,1,\dots ,1) \in \mathbb {S}^{n-1}$$. The large deviation principle (LDP) for such projections as $$n\rightarrow \infty$$ is given by the classical Cramer’s theorem. We prove an LDP… CONTINUE READING

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