Speaker: Lung-Chi Chen (Fu-Jen Catholic University)
Title: Asymptotic behavior of the critical two-point functions for long-range statistical-mechanical models
Time: 2010-07-29 (Thu.)  15:00 - 16:00
Place: Auditorium, 6 Floor, Institute of Mathematics (NTU Campus)
Abstract: In this talk, we consider random walk and various statistical-mechanical models (such as self-avoiding walk, oriented percolation and percolation) that are defined by the $\mathbb{Z}^d$-symmetric probability distribution $D$. Suppose that the function $D(x)$ decays as $|x|^{-d-\alpha}$ with $\alpha>0$, We show that, for random walk with $d>\min\{\alpha,2\}$ and for the other models with $d$ bigger than the model-dependent upper-critical dimension, the critical two-point function decays as $|x|^{\min\{\alpha,2\}-d}$. The talk is based on joint work in progress with Akira Sakai.
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