AI 中文总结
研究多物种开放边界TASEP平稳分布公式的问题，利用C型Kirillov - Reshetikhin晶体构建C型多线队列及配对算法，得到α = β = 1时该TASEP平稳分布的组合公式。
AI 中文摘要
具有开放边界的完全非对称简单排斥过程（TASEP）是一个有限马尔可夫链，描述粒子在一维晶格上相邻位置间跳跃，左右边界转移由参数α和β控制。多物种TASEP是其高阶推广，粒子有不同种类。Ferrari和Martin（2007）引入多线队列来计算圆上多物种TASEP的平稳分布。找到多物种开放边界TASEP平稳分布的组合公式仍是未解决问题。利用C型Kirillov - Reshetikhin晶体，我们构建了C型多线队列及相应的Ferrari - Martin配对算法，将其投影到TASEP配置上。这为α = β = 1特化的多物种开放边界TASEP的平稳分布给出了组合公式。
英文摘要
The totally asymmetric simple exclusion process (TASEP) with open boundaries is a finite Markov chain describing particles hopping between adjacent sites on a one-dimensional lattice with left and right boundary transitions governed by parameters $α$ and $β$. The multispecies TASEP is a higher-rank generalization in which particles have different species. Multiline queues were introduced by Ferrari and Martin (2007) to compute the stationary distribution of the multispecies TASEP on a circle. It has remained an open problem to find a combinatorial formula for the stationary distribution of the multispecies open-boundary TASEP. Using Kirillov--Reshetikhin crystals of type $C$, we construct type $C$ multiline queues and a corresponding Ferrari--Martin pairing algorithm that projects them to TASEP configurations. This yields a combinatorial formula for the stationary distribution of the multispecies open-boundary TASEP for the $α=β=1$ specialization.
