标题： ASEP和确定点过程 显示英文标题

标题： The ASEP and determinantal point processes

摘要： 我们介绍了一类与实线上正交多项式相关的离散行列式点过程，其关联核由相应的雅可比矩阵的谱投影定义。 对于经典的权函数，我们展示了这些过程如何作为各种超几何正交多项式过程的极限出现。 然后我们证明了具有阶梯初始条件的ASEP的高度函数的q-拉普拉斯变换等于离散拉盖尔系综上一个简单乘法泛函的期望值——这是新家族中的一个成员。 这使得我们可以得到ASEP在三种极限情况下的长时间渐近行为：(a)有限多个最右边粒子；(b) 高度函数的GUE Tracy-Widom渐近；(c)弱不对称ASEP的高度函数的KPZ渐近。 我们还给出了四分之一平面上两个随机六顶点模型实例的类似结果。 这些证明基于相应行列式点过程的极限过渡。 显示英文摘要

摘要： We introduce a family of discrete determinantal point processes related to orthogonal polynomials on the real line, with correlation kernels defined via spectral projections for the associated Jacobi matrices. For classical weights, we show how such ensembles arise as limits of various hypergeometric orthogonal polynomials ensembles. We then prove that the q-Laplace transform of the height function of the ASEP with step initial condition is equal to the expectation of a simple multiplicative functional on a discrete Laguerre ensemble --- a member of the new family. This allows us to obtain the large time asymptotics of the ASEP in three limit regimes: (a) for finitely many rightmost particles; (b) GUE Tracy-Widom asymptotics of the height function; (c) KPZ asymptotics of the height function for the ASEP with weak asymmetry. We also give similar results for two instances of the stochastic six vertex model in a quadrant. The proofs are based on limit transitions for the corresponding determinantal point processes.