Scaling Limits for Non-intersecting Polymers and Whittaker Measures

被引:7
|
作者
Johnston, Samuel G. G. [1 ]
O'Connell, Neil [2 ]
机构
[1] Karl Franzens Univ Graz, Inst Math & Wissensch Rechnen, A-8010 Graz, Austria
[2] Univ Coll Dublin, Sch Math & Stat, Dublin 4, Ireland
基金
欧洲研究理事会;
关键词
Non-intersecting paths; Polymers; Whittaker measures; Stochastic interfaces;
D O I
10.1007/s10955-020-02534-y
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
We study the partition functions associated with non-intersecting polymers in a random environment. By considering paths in series and in parallel, the partition functions carry natural notions of subadditivity, allowing the effective study of their asymptotics. For a certain choice of random environment, the geometric RSK correspondence provides an explicit representation of the partition functions in terms of a stochastic interface. Formally this leads to a variational description of the macroscopic behaviour of the interface and hence the free energy of the associated non-intersecting polymer model. At zero temperature we relate this variational description to the Marcenko-Pastur distribution, and give a new derivation of the surface tension of the bead model.
引用
收藏
页码:354 / 407
页数:54
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