The TASEP speed process.
The TASEP speed process.
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TASEP 加快进程。
DOI：
10.1214/10-aop561
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发表时间：
2008
影响因子：
2.3
通讯作者：
Benedek Valk'o
中科院分区：
文献类型：
--
作者：
Gideon Amir;Omer Angel;Benedek Valk'o
在多类型完全不对称简单排斥过程（TASEP）中，Z的每一个位点都被一个标记粒子占据，如果两个相邻的标记粒子的标记顺序是递增的，那么它们之间的交换速率为1.考虑具有初始配置的过程，其中每个粒子由其位置标记。据了解，在这种情况下，每个粒子的渐近速度均匀分布在[-1，1]上。我们研究这些速度的联合分布：TASEP速度过程。我们证明了TASEP速度过程是多类型TASEP动态的平稳测度。因此，我们可以把每个遍历平稳测度描述为速度过程测度的投影。这概括了以前的描述限制到100多个类。通过结合这一结果与已知的固定措施TASEP与许多类型，我们计算几个边际的速度过程中，包括联合密度的两个和三个连续的速度。该分布的一个显著性质是，两个速度相等的概率为正，并且对于任何给定的粒子，有无穷m个其他粒子具有相同的速度。我们还研究了（部分）不对称简单排斥过程（ASEP）。我们证明了上述初始配置的ASEP的状态，看作是Z的排列，是对称的分布。这使得我们可以将我们的一些结果，包括平稳性和描述所有遍历平稳测度，也ASEP。
In the multi-type totally asymmetric simple exclusion process (TASEP), each site ofZ is occupied by a labeled particle, and two neighboring particles are int erchanged at rate one if their labels are in increasing order. Consider the process with the initial con figuration where each particle is labeled by its position. It is known that in this case a.s. each particle has an asymptotic speed which is distributed uniformly on [−1, 1]. We study the joint distribution of these speeds: the TASEP speed process. We prove that the TASEP speed process is a stationary measure for the multi-type TASEP dynamics. Consequently, we can describe every ergodic stationary measure as a projection of the speed process measure. This generalizes previous descriptions restricted to finitely many classes. By combining this result with known stationary measures for TASEPs with finitely many types we compute several marginals of the speed process, including the joint density of two and three consecutive speeds. One striking property of the distribut ion is that two speeds are equal with positive probability and for any given particle there are infinitely m any others with the same speed. We also study the (partially) asymmetric simple exclusion process (ASEP). We prove that the states of the ASEP with the above initial configuration, seen as permutations ofZ, are symmetric in distribution. This allows us to extend some of our results, i ncluding the stationarity and description of all ergodic stationary measures, also to the ASEP.
DOI：
10.1214/08-aap542
发表时间：
2009
期刊：
The Annals of Applied Probability
影响因子：
--
作者：
Ferrari P
通讯作者：
Ferrari P
DOI：
10.1214/08-aihp303
发表时间：
2009
期刊：
Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
影响因子：
--
作者：
Ferrari P
通讯作者：
Ferrari P
多类 Hammersley-Aldous-Diaconis 流程和多类客户队列
DOI：
10.1214/08-aihp168
发表时间：
2009
期刊：
Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
影响因子：
--
作者：
Ferrari P
通讯作者：
Ferrari P