# Talk:Probability of large deviations

The article is quite obsolete, as is noted in its "Comments" section. Some literature is given in that section, but a number of more recent books should be used, too.

Nowadays large deviations are usually understood as *logarithmic* asymptotics of small probabilities in the region where the normal approximation fails even on the logarithmic level. The theory is formulated in terms of rate functions; terribly, rate function is not mentioned at all in our encyclopedia! The more narrow region where probabilities are small but the normal approximation holds on the logarithmic level is well-known as *moderate deviations* (only mentioned twice in our encyclopedia: in "Wiener sausage" and "Intermediate efficiency".

Thus, a complete rewrite is desirable.

By the way, Srinivasa S. R. Varadhan was awarded the Abel Prize (2007) "for his fundamental contributions to probability theory and in particular for creating a unified theory of large deviations".

--Boris Tsirelson 16:51, 25 April 2012 (CEST)

**How to Cite This Entry:**

Probability of large deviations.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Probability_of_large_deviations&oldid=25428