Directed polymers in a random environment: Some results on fluctuations
Directed polymers in a random environment: Some results on fluctuations
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随机环境中的定向聚合物：波动的一些结果
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发表时间：
1997
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通讯作者：
M. S. T. Piza
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文献类型：
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作者：
M. S. T. Piza
我们考虑了一个关于n +d的聚合物模型，其中每个边都与一个随机变量v（e）相关联。聚合物构型由有向路径r表示，权重为exp[-β ∑e∈rν（e）]，其中β=1/T为温度的倒数。我们扩展了一些严格的结果，已经获得了基态的这个模型的有限温度。特别地，我们得到了样品间自由能涨落的上、下界，以及描述自由能涨落的指数与聚合物构型的横向位移之间的严格标度不等式
We consider a polymer model on ℤ+d where to each edgee is associated a random variable v(e). A polymer configuration is represented by a directed pathr and has a weight exp[-β ∑e∈rν(e)], withβ=1/T the inverse temperature. We extend some rigorous results that have been obtained for the ground state of this model to finite temperatures. In particular we obtain some upper and lower bounds on sample-to-sample free energy fluctuations, and also rigorous scaling inequalities between the exponents describing free energy fluctuations and transversal displacements of polymer configurations