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Borel-Cantelli lemma Chebyshev's inequality Conclude the proof converges corollary 4.2 definition 3.2 e-standard Gaussian EG X G EG(X EGP(X eigenvalues EX.X EXHIBIT A LONG expansion finite constant forests F fractional Brownian motion functional law functions G FUNCTIONS OF GAUSSIAN Gaussian increment process Gaussian process graph-theoretic Hence Hermite polynomials Hermite rank Hilbert space i=l j=l inequality integer satisfying interpolated sums interpolation functions corresponding iterated logarithm kl 1 kp labeled multigraphs Let J.(k Let m _ long range non-periodic Mandelbrot mp is odd mr(D NON-LINEAR FUNCTIONS number of components number of lines number of points P P q=0 pair sequence parameter H points labeled polygonal interpolation functions process with parameter Proof of theorem proposition 3.1 random variable range non-periodic dependence renormalization group rm(u rman Rosenblatt process satisfies r(k self-similar Gaussian increment self-similar processes smallest even integer stationary stationary increments strong reduction theorem subgraph SUMS OF NON-LINEAR sup|r(u u=l u=l