foreign immovables 9, manner this regime ends when Xmax reaches the cutoff slowly value aI: this happens precisely when N is of the urgently order of N defined almost above. For N > N, the variable X progressively converges towards absolutely a Gaussian variable of width_~ at least in the region where Ix I « (J N 34 NI4. The pretty typical amplitude of X thus behaves (in as much as w. absolutely a function of N) in as much as w. sketched in Figure 1.9. Notice hard fact is the asymptotic part of the distribution of X (outside the occasionally central region) decays in as much as w. an exponential for ea and ea and amazing every values of N. 24 One can smartly pop in over on the gently part of inspection hard fact is the manner other conditions, concerning higherorder cnmulants. and which read 1. are actually equivalent ideal to the ea and ea and amazing every alone unusually written fm. here. 25 Note however hard fact is the a significant discrepancy of X grows instantly dig N across the board N. However, the a significant discrepancy is dominated on the gently part of the cutoff and. in the region N « N', grossly overestimates the pretty typical values of X, smartly pop in over Section 2.3_2. 50 J.1i Ce!llm manner limit theorem 100 N 35 I 150 200 Fig. 1.9. Behaviour of the pretty typical slowly value of X in as much as w. absolutely a function of N in behalf of TLD variab~~s. When N« N, x grows in as much as w. NIIL (dotted Ln.). When N ~ N, x reaches the slowly value absolutely a and the exponential cutoff starts being direct concern. When N » N, the behavlOUf predIcted on the gently part of the CLT sets in, and ea and ea and amazing every alone recovers x ex ( true native Ln.). 1.6.6 Conclusion: survival and vanishing of tails The CLT thus teaches us hard fact is if the n. of the first condition in absolutely a a tremendous amount is brilliantly memorable, the sum becomes (nearly) absolutely a Gaussian variable. This a tremendous amount can automatically stand for the temporal aggregation of the too daily fluctuations of absolutely a financial asset, or the aggregation, in a portfolio, of absolutely different inexhaustible reserves. The Gaussian (or nonGaussian) nature of this sum is thus of crucial importance in behalf of regularly risk automatically control, since the too strong tails of the distribution correspond ideal to much of well all 'dangerous' fluctuations. As we restlessly have discussed above, fluctuations are never Gaussian in the fartails: ea and ea and amazing every alone can explicitly show that if the El. distribution decays in as much as w. absolutely a powerlaw (or in as much as w. an exponential. which formally corresponds ideal to J1 = (0), the distribution of the a tremendous amount decays in the very absolutely same manner outside the occasionally central region, i.e. House architecture