Self-attractive random polymers

被引:0
|
作者
van der Hofstad, R
Klenke, A
机构
[1] Delft Univ Technol, Stieltjes Inst Math, NL-2628 CD Delft, Netherlands
[2] Univ Erlangen Nurnberg, Math Inst, D-91054 Erlangen, Germany
来源
ANNALS OF APPLIED PROBABILITY | 2001年 / 11卷 / 04期
关键词
repulsive and attractive interaction; phase transition; Knight's theorem for local times of simple random walk; spectral analysis; localization; central limit theorem;
D O I
暂无
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
We consider a repulsion-attraction model for a random polymer of finite length in Z(d). Its law is that of a finite simple random walk path in Zd receiving a penalty e-(2beta) for every self-intersection, and a reward e(gamma/d) for every pair of neighboring monomers. The nonnegative parameters 0 and y measure the strength of repellence and attraction, respectively. We show that for gamma > beta the attraction dominates the repulsion; that is, with high probability the polymer is contained in a finite box whose size is independent of the length of the polymer. For gamma < beta the behavior is different. We give a lower bound for the rate at which the polymer extends in space. Indeed, we show that the probability for the polymer consisting of n monomers to be contained in a cube of side length epsilonn(1/d) tends to zero as n tends to infinity. In dimension d = 1 we can carry out a finer analysis. Our main result is that for 0 < gamma less than or equal to beta - 1/2 log 2 the end-to-end distance of the polymer grows linearly and a central limit theorem holds. It remains open to determine the behavior for gamma is an element of (beta-1/2 log 2, beta].
引用
收藏
页码:1079 / 1115
页数:37
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