论文标题
KPZ制度中ASEP的动力相变
Dynamical Phase Transition of ASEP in the KPZ regime
论文作者
论文摘要
我们考虑$ \ mathbb {z} $上的非对称简单排除过程（ASEP）。对于连续的密度，ASEP在局部平衡中很大，但是在不连续性的情况下，人们期望看到动态的相变，即不同平衡的混合物。我们考虑使用确定性初始数据的ASEP，以便在很大程度上，两个稀有因素在原点汇聚在一起，密度从$ 0 $上升到$ 1 $。在KPZ $ 1/3 $比例尺上转移该度量，我们表明ASEP定律仅将孔均匀地汇总为Dirac措施的混合物。只有颗粒。该混合物的参数是将第二类粒子分布成两个独立GUE的差异的概率。应将其与1994年的法拉利和字体的结果进行比较，\ 1994 \ cite {ff94b}，他们以随机初始数据造成的不连续性获得了Bernoulli产品测量的混合物，而GUES被高斯人代替。
We consider the asymmetric simple exclusion process (ASEP) on $\mathbb{Z}$. For continuous densities, ASEP is in local equilibrium for large times, at discontinuities however, one expects to see a dynamical phase transition, i.e. a mixture of different equilibriums. We consider ASEP with deterministic initial data such that at large times, two rarefactions come together at the origin, and the density jumps from $0$ to $1$. Shifting the measure on the KPZ $1/3$ scale, we show that the law of ASEP converges to a mixture of the Dirac measures with only holes resp. only particles. The parameter of that mixture is the probability that the second class particle, which is distributed as the difference of two independent GUEs, stays to the left of the shift. This should be compared with the results of Ferrari and Fontes from 1994 \cite{FF94b}, who obtained a mixture of Bernoulli product measures at discontinuities created by random initial data, with the GUEs replaced by Gaussians.
