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