高維度下具長域自我相斥隨機漫步，滲流與 Ising模型的兩點函數之臨界行為

Abstract

在這此次計劃中， 我研究重心放在研究在高維度下具長域定向滲流，自我相斥隨機漫步與Ising 模型之兩點函數的臨界與漸進行為，此問題是與北海道大學數學系Akira Sakai教授合作的文章， 我們獲得兩點函數在臨界行為的收斂速度與漸進行為，並於2015年刊登在Ann. Prob. 期刊上，並且我們持續研究此類問題。 此外本人與成大物理系張書銓教授探討在二維三角晶格與蜂窩狀晶格上特殊的定向滲流之兩點函數的臨界行為與收斂速度也有兩篇文章分別發表于 J. Stat. Phys. 和 Physica A， 我們獲得在特殊的模型下兩點函數之收斂速度的上界估計與下界估計的結果，並且我們也持續研究此類的問題。

In this project, my main research is focused on the critical two-point functions for long-range percolation, self-avoiding walk and Ising model in high dimensions. This is joint work with professor Akira Sakai in the mathematics department at Hokkaido university. We obtained the rate of convergence and asymptotic behavior of two point functions and it has been published at Journal of ann. Probab. In 2015. We are doing this kind of problem now. In addition, I and professor Shu-Chiuan Chang in the physics department at national Cheng Kung university have some results for a version of directed percolation on the triangle lattice and honeycomb lattice. We obtained the upper and lower bounds of two point functions and our results bas been published J. Stat. Phys. and Physica A. I are doing the similar problems now.