具有冲击和稀疏扇的TASEP的极限过程
Limit processes for TASEP with shocks and rarefaction fans
摘要：
本文研究了具有双侧Bernoulli初始条件的完全非对称简单排除过程（TASEP），具有左密度rho_-和右密度rho_+。我们考虑相关的高度函数，其离散梯度由粒子出现给出。宏观上，根据rho_{+/-}的值，激波或稀疏扇形具有确定的极限形状。我们的特点作为密度rho_{+/-}和不同的宏观区域的函数的波动的大时间尺度限制。此外，利用一种缓慢的去相关现象，将结果从固定时间推广到整个时空，除了某些方向（相关Burgers方程的特征解）上的问题仍然是开放的。在证明TASEP结果的过程中，我们得到了一类具有外源的角增长过程的涨落的极限过程，等价地得到了具有双边边界条件的有向渗流模型的末次通过时间的极限过程.此外，我们提供类似的结果扰动复杂的Wishart（样本协方差）矩阵的特征值。
英文摘要：
We consider the totally asymmetric simple exclusion process (TASEP) with two-sided Bernoulli initial condition, i.e., with left density rho_- and right density rho_+. We consider the associated height function, whose discrete gradient is given by the particle occurrences. Macroscopically one has a deterministic limit shape with a shock or a rarefaction fan depending on the values of rho_{+/-}. We characterize the large time scaling limit of the fluctuations as a function of the densities rho_{+/-} and of the different macroscopic regions. Moreover, using a slow decorrelation phenomena, the results are extended from fixed time to the whole space-time, except along the some directions (the characteristic solutions of the related Burgers equation) where the problem is still open. On the way to proving the results for TASEP, we obtain the limit processes for the fluctuations in a class of corner growth processes with external sources, of equivalently for the last passage time in a directed percolation model with two-sided boundary conditions. Additionally, we provide analogous results for eigenvalues of perturbed complex Wishart (sample covariance) matrices.
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