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Download An elementary introduction to large deviations
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Transcript
0 -0.5 ln P( Mn/n > 0.6 ) -1 -1.5 -2 -2.5 -3 -3.5 -4 -4.5 10 20 30 40 0 50 n 60 70 80 90 70 80 90 100 -0.05 ln P( Mn/n > 0.6 ) /n -0.1 -0.15 -0.2 -0.25 -0.3 -0.35 -0.4 10 20 30 40 50 n 60 100 Figure 8: The distribution of the mean for coin-tossing: ln P( Mn > 0.6 ) (top) is super-additive and so ln P( Mn > 0.6 ) /n (bottom) is approximately monotone; as n increases, ln P( Mn > 0.6 ) /n converges to its maximum value. 24
