Gaussian fluctuations of replica overlap in directed polymers
Gaussian fluctuations of replica overlap in directed polymers
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DOI：
10.1214/22-ecp476
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发表时间：
2022-01
影响因子：
0.5
通讯作者：
Yu Gu;T. Komorowski
中科院分区：
文献类型：
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作者：
Yu Gu;T. Komorowski
。在这篇简短的文章中，我们证明了在高斯随机环境、低温状态和所有维度中布朗定向聚合物的复制重叠类型的中心极限定理。该证明依赖于由空间缓和噪声驱动的 KPZ 方程的超浓缩结果，该结果受到 Chatterjee 最近工作的启发 [14]。
. In this short note, we prove a central limit theorem for a type of replica overlap of the Brownian directed polymer in a Gaussian random environment, in the low temperature regime and in all dimensions. The proof relies on a superconcentration result for the KPZ equation driven by a spatially mollified noise, which is inspired by the recent work of Chatterjee [14].