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| | 18.325 Spring 2001 Bazant, Lecture Notes |
 | | Fisher-Tippett theory of limiting distributions for extremes of independent random variables, Central Limit Theorem for supercritical percolation, self-similar "fractal CLT" at the critical point, saddle-point approximation, RG prediction of crossover and the strength of the infinite cluster in the supercritical regime. |
| | Finish derivation of additivity of power-law tail amplitudes, asymptotic expansions and Laurent series for symmetric Levy densities, statistics of the largest step size (out of n steps) for exponential and power-law tails, Fisher-Tippett distribution, connection between extreme events and divergent moments. |
| | Asymptotics of the position distribution of the "student-t walk", p(x) = A/(1+x^2)^2, with a dominant power-law tail from the end-point at the origin and a central Gaussian from a nonzero saddle point in the integrand of the inverse Fourier transform. |
| www-math.mit.edu /~bazant/teach/18.325/lectures (823 words) |
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