Lattice Versus Tree
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- 刊名：Lecture Notes in Mathematics
- 出版年：2017
- 出版时间：2017
- 年：2017
- 卷：2175
- 期：1
- 页码：57-73
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14. Mathematics, case 7012, Université Paris Diderot - Paris 7, Paris, France - 丛书名：Directed Polymers in Random Environments
- ISBN：978-3-319-50487-2
- 卷排序：2175
文摘
In this chapter we deal with polymer models on different oriented graphs and compare them with the lattice case. As revealed by Derrida and Spohn in, many interesting questions can be answered on the regular tree. Later on, refined tree-like structures including Derrida’s m-tree has been introduced, yielding further comparisons. There, correlations are simpler compared to the lattice case, since the medium along two paths becomes independent as soon as they visit different sites. In the sense of simplifying the correlation structure, these models play the role of mean-field models.