Subgaussian concentration and rates of convergence in directed polymers
Subgaussian concentration and rates of convergence in directed polymers
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定向聚合物中的亚高斯浓度和收敛速率
DOI：
10.1214/ejp.v18-2005
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发表时间：
2012
影响因子：
1.4
通讯作者：
Nikos Zygouras
中科院分区：
文献类型：
--
作者：
K. S. Alexander;Nikos Zygouras
我们考虑在$(d+1)$维上具有接近Gamma I.I.D.的定向随机聚合物。无序。我们研究了配分函数$Z_N，\omega}，建立了次高斯标度下关于它的平均值的指数稠密性。这用来表明$\mathbb{E}[\log Z_{N，\omega}]$与自由能乘以$N的差额也是次高斯量(即$o(\sqrt{N})$)，具体地说是$O(\sqrt{FRAC{N}{\logN}}\log\logN)$
We consider directed random polymers in $(d+1)$ dimensions with nearly gamma i.i.d. disorder. We study the partition function $Z_{N,\omega}$ and establish exponential concentration of $\log Z_{N,\omega}$ about its mean on the subgaussian scale $\sqrt{N/\log N}$ . This is used to show that $\mathbb{E}[ \log Z_{N,\omega}]$ differs from $N$ times the free energy by an amount which is also subgaussian (i.e. $o(\sqrt{N})$), specifically $O( \sqrt{\frac{N}{\log N}}\log \log N)$
影响因子：
2.5
作者：
Corwin, Ivan;O'Connell, Neil;Zygouras, Nikolaos
通讯作者：
Zygouras, Nikolaos