Generalized determinant solution of the discrete-time totally asymmetric exclusion process and zero-range process.
Generalized determinant solution of the discrete-time totally asymmetric exclusion process and zero-range process.
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离散时间完全不对称排除过程和零范围过程的广义行列式解。
DOI：
10.1103/physreve.69.066136
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
R. V. Shelest
中科院分区：
文献类型：
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作者：
J. Brankov;V. Priezzhev;R. V. Shelest
我们考虑了无限长链上有限个粒子服从完全不对称排斥过程的离散时间演化。我们的第一个结果是在给定的初始和最终位置找到粒子的条件概率的行列式表达式，假设它们同时开始和结束。该表达式的形式与J.Stat得到的表达式相同。太棒了。88,427(1997)]用于连续时间进程。其次，我们证明了在一些充分条件下，行列式表达式可以推广到粒子在其各自的时刻开始和结束的情况。后一个结果被用来求解具有开边界的有限链上的非平稳零值过程。
We consider the discrete-time evolution of a finite number of particles obeying the totally asymmetric exclusion process with backward-ordered update on an infinite chain. Our first result is a determinant expression for the conditional probability of finding the particles at given initial and final positions, provided that they start and finish simultaneously. The expression has the same form as the one obtained by J. Stat. Phys. 88, 427 (1997)] for the continuous-time process. Next we prove that under some sufficient conditions the determinant expression can be generalized to the case when the particles start and finish at their own times. The latter result is used to solve a nonstationary zero-range process on a finite chain with open boundaries.
相互作用的布朗粒子的零温度限制，II._一维凝固。
DOI：
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发表时间：
2004
期刊：
Ann. Probab. 32
影响因子：
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作者：
Hiromitsu Suetani;Takehiko Horita;Shin Mizutani;T.Funaki
通讯作者：
T.Funaki