TASEP的电流涨落：Prähofer-Spohn猜想的证明
Current fluctuations for TASEP: A proof of the Prähofer--Spohn conjecture
摘要：
我们认为家庭的双侧伯努利初始条件TASEP，作为左，右密度（$ρ_-,ρ_+$）是不同的，引起冲击波和稀疏风扇-这两个现象是典型的TASEP。我们证明了[Progr.可能吧51（2002）185- 204]，其根据两个密度$ρ_-,ρ_+$和速度$y$来表征双侧TASEP的高度函数的波动的阶数和缩放函数，在所述速度周围观察高度。在证明TASEP的这个定理的同时，我们还证明了一类带外源的角增长过程的涨落定理，或者等价地证明了具有双边边界条件$ρ_-$和$1-ρ_+$的有向末次通过渗流模型的末次通过时间的涨落定理.我们提供了一个完整的表征的顺序和该模型的最后通过时间$L(N,M)$的波动作为三个参数的函数的标度函数：两个边界/源率$ρ_-$和$1-ρ_+$，和标度比$γ^2=M/N$。该定理的证明利用了[Comm.Math.Phys.265（2006）1- 44]的结果和[Ann. Probab. 33（2005）1643--1697]关于随机矩阵理论中Wishart系综的有限秩扰动。
英文摘要：
We consider the family of two-sided Bernoulli initial conditions for TASEP which, as the left and right densities ($ρ_-,ρ_+$) are varied, give rise to shock waves and rarefaction fans---the two phenomena which are typical to TASEP. We provide a proof of Conjecture 7.1 of [Progr. Probab. 51 (2002) 185--204] which characterizes the order of and scaling functions for the fluctuations of the height function of two-sided TASEP in terms of the two densities $ρ_-,ρ_+$ and the speed $y$ around which the height is observed. In proving this theorem for TASEP, we also prove a fluctuation theorem for a class of corner growth processes with external sources, or equivalently for the last passage time in a directed last passage percolation model with two-sided boundary conditions: $ρ_-$ and $1-ρ_+$. We provide a complete characterization of the order of and the scaling functions for the fluctuations of this model's last passage time $L(N,M)$ as a function of three parameters: the two boundary/source rates $ρ_-$ and $1-ρ_+$, and the scaling ratio $γ^2=M/N$. The proof of this theorem draws on the results of [Comm. Math. Phys. 265 (2006) 1--44] and extensively on the work of [Ann. Probab. 33 (2005) 1643--1697] on finite rank perturbations of Wishart ensembles in random matrix theory.
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