Convergence of lattice trees to super-Brownian motion above the critical dimension
نویسنده
چکیده
We use the lace expansion to prove asymptotic formulae for the Fourier transforms of the r-point functions for a spread-out model of critically weighted lattice trees in Z for d > 8. A lattice tree containing the origin defines a sequence of measures on Z, and the statistical mechanics literature gives rise to a natural probability measure on the collection of such lattice trees. Under this probability measure, our results, together with the appropriate limiting behaviour for the survival probability, imply convergence to super-Brownian excursion in the sense of finite-dimensional distributions .
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