Large Deviation Theory
نویسنده
چکیده
If we draw a random variable n times from Q, the probability distribution of the sum of the random variables is given by Q. This is the convolution of Q with itself n times. As n → ∞, Q tends to a normal distribution by the central limit theorem. This is shown in Figure 1. The top line is a computed normal distribution with the same mean as Q. However, as shown in Figure 3, when plotted on a log scale it becomes clear that the tails of the distribution are not “normal”. They are stable for increasing n, and large deviation theory provides a method for computing the tails exactly. 0 0.001 0.002 0.003 0.004 0.005 0.006
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