Free Energy Fluctuations for Directed Polymers in Random Media in 1 C 1 Dimension
Free Energy Fluctuations for Directed Polymers in Random Media in 1 C 1 Dimension
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DOI：
10.1002/cpa.21520
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发表时间：
2014-07-01
影响因子：
3
通讯作者：
Ferrari, Patrik
中科院分区：
文献类型：
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作者：
Borodin, Alexei;Corwin, Ivan;Ferrari, Patrik
考虑了两种时空无关随机介质中的定向聚合物模型（O 'Connell-Yor半离散定向聚合物和连续定向无规聚合物），通过对它们配分函数的拉普拉斯变换的精确Fredholm行列式公式的渐近分析，证明了它们在正温度下的KPZ普适性.特别是，我们表明，对于大的时间，自由能波动的概率分布，当重新缩放（1/3），收敛到GUE Tracy-Widom分布。我们还考虑了边界扰动对淬灭随机介质极限自由能统计的影响。对于半离散定向聚合物，当形成淬灭随机介质的有限数量的布朗运动的漂移被严格调谐时，统计数据反而由来自尖峰随机矩阵理论的限制性Baik-Ben Arous-Peche分布支配。对于连续介质聚合物，边界扰动对应于从特定类中选择随机热方程的初始数据，同样对于它的连续介质Kardar-Parisi-Zhang方程也是如此。我们证明的拉普拉斯变换公式可以被反演，以给出这些随机偏微分方程的解的单点概率分布。(c)2014 Wiley Periodicals，Inc.
We consider two models for directed polymers in space-time independent random media (the O'Connell-Yor semidiscrete directed polymer and the continuum directed random polymer) at positive temperature and prove their KPZ universality via asymptotic analysis of exact Fredholm determinant formulas for the Laplace transform of their partition functions. In particular, we show that for large time , the probability distributions for the free energy fluctuations, when rescaled by (1/3), converges to the GUE Tracy-Widom distribution. We also consider the effect of boundary perturbations to the quenched random media on the limiting free energy statistics. For the semidiscrete directed polymer, when the drifts of a finite number of the Brownian motions forming the quenched random media are critically tuned, the statistics are instead governed by the limiting Baik-Ben Arous-Peche distributions from spiked random matrix theory. For the continuum polymer, the boundary perturbations correspond to choosing the initial data for the stochastic heat equation from a particular class, and likewise for its logarithmthe Kardar-Parisi-Zhang equation. The Laplace transform formula we prove can be inverted to give the one-point probability distribution of the solution to these stochastic PDEs for the class of initial data. (c) 2014 Wiley Periodicals, Inc.