PushTASEP in inhomogeneous space
PushTASEP in inhomogeneous space
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DOI：
10.1214/20-ejp517
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发表时间：
2019-10
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通讯作者：
L. Petrov
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文献类型：
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作者：
L. Petrov
考虑了非均匀空间中具有阶跃初始组态的PushTASEP（pushtotally asymmetric simple exclusion process，有时也称为long-range TASEP）。也就是说，每个粒子跳跃的速率取决于该粒子的位置。我们匹配这个PushTASEP与舒尔过程的高度函数的分布。利用这种匹配和Schur过程的行列式结构，我们得到了Kardar-Parisi-Zhang普适类中随机粒子系统的极限形状和波动结果。PushTASEP是通常的TASEP的近亲。在非齐次空间中，前者是可积的，而后者的可积性未知。
We consider the PushTASEP (pushing totally asymmetric simple exclusion process, also sometimes called long-range TASEP) with the step initial configuration evolving in an inhomogeneous space. That is, the rate of each particle's jump depends on the location of this particle. We match the distribution of the height function of this PushTASEP with Schur processes. Using this matching and determinantal structure of Schur processes, we obtain limit shape and fluctuation results which are typical for stochastic particle systems in the Kardar-Parisi-Zhang universality class. PushTASEP is a close relative of the usual TASEP. In inhomogeneous space the former is integrable, while the integrability of the latter is not known.