Random-walk in Beta-distributed random environment
Random-walk in Beta-distributed random environment
复制标题
Beta 分布随机环境中的随机游走
DOI：
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
Ivan Corwin
中科院分区：
文献类型：
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作者：
Guillaume Barraquand;Ivan Corwin
我们引入了一个随机环境中精确可解的随机漫步模型，我们称之为Beta RWRE。这是$$mathbb {Z}$$Z中的随机游走，它执行最近邻跳跃，并根据Beta分布绘制转移概率。我们还描述了一个相关的定向聚合物模型，它是q-Hahn相互作用粒子系统的一个极限。用Fredholm行列式表示步行者位置的淬灭概率分布函数，证明了步行者位置满足的大偏差原理的二阶立方根尺度修正，并收敛到Tracy-Widom分布。我们还证明了这个极限定理可以用强相关随机变量的最大值来解释：独立步行者在同一环境中的位置。β RWRE的零温度对应物可以并行研究。我们还证明了该模型的Tracy-Widom极限定理。
We introduce an exactly-solvable model of random walk in random environment that we call the Beta RWRE. This is a random walk in $$mathbb {Z}$$Z which performs nearest neighbour jumps with transition probabilities drawn according to the Beta distribution. We also describe a related directed polymer model, which is a limit of the q-Hahn interacting particle system. Using a Fredholm determinant representation for the quenched probability distribution function of the walker’s position, we are able to prove second order cube-root scale corrections to the large deviation principle satisfied by the walker’s position, with convergence to the Tracy–Widom distribution. We also show that this limit theorem can be interpreted in terms of the maximum of strongly correlated random variables: the positions of independent walkers in the same environment. The zero-temperature counterpart of the Beta RWRE can be studied in a parallel way. We also prove a Tracy–Widom limit theorem for this model.
影响因子：
3
作者：
Borodin, Alexei;Corwin, Ivan;Ferrari, Patrik
通讯作者：
Ferrari, Patrik
具有伽马分布权重的随机聚合物模型的 Tracy-Widom 渐近
影响因子：
1.4
作者：
O'Connell N
通讯作者：
O'Connell N