作者：Sly, Allan; Heyde, Chris
作者单位：University of California System; University of California Berkeley; Australian National University; Columbia University
摘要：We consider functionals of long-range dependent Gaussian sequences with infinite variance and obtain nonstandard limit theorems. When the long-range dependence is strong enough, the limit is a Hermite process, while for weaker long-range dependence, the limit is alpha-stable Levy motion. For the critical value of the long-range dependence parameter, the limit is a sum of a Hermite process and alpha-stable Levy motion.
作者：Hara, Takashi
作者单位：Kyushu University
摘要：We consider nearest-neighbor self-avoiding walk, bond percolation, lattice trees, and bond lattice animals on Z(d). The two-point functions of these models are respectively the generating function for self-avoiding walks from the origin to x epsilon Z(d), the probability of a connection from the origin to x, and the generating functions for lattice trees or lattice animals containing the origin and x. Using the lace expansion, we prove that the two-point function at the critical point is asymp...
