发表机构
King’s College London（伦敦国王学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究马尔可夫过程中排斥与非碰撞两种粒子动力学的等价性，通过指数鞅测度变换建立联系，推广了环上 TASEP 与条件非碰撞游走者的已知结果。
AI 中文摘要
设 $(\xi_t)_{t \geq 0}$ 为在可数状态空间 $E$ 上取值的连续时间马尔可夫过程。我们考虑从不同初始位置出发的 $k$ 个 $\xi$ 副本，并记 $X = (X_t)_{t \geq 0}$ 为在 $E^k$ 中产生的构型过程。我们比较粒子之间的两种相互作用形式：第一种是条件化粒子永不碰撞（非碰撞动力学），第二种是简单地关闭任何会导致两个粒子占据同一位置的跳跃（排斥动力学）。在碰撞时间尾部概率的温和条件下，我们证明这两种动力学通过一个显式的指数鞅测度变换相互关联。这推广了可积概率文献中一个近期结果，该结果将环上的 TASEP 与条件为永不碰撞的非对称游走者联系起来。
英文摘要
Let $(ξ_t)_{t \geq 0}$ be a continuous-time Markov process taking values in a countable state space $E$. We consider $k$ copies of $ξ$ started from distinct positions, and write $X = (X_t)_{t \geq 0}$ for the resulting process of configurations in $E^k$. We compare two forms of interaction between the particles: the first is conditioning the particles to never collide (noncolliding dynamics), and the second is simply switching off any jumps that would cause two particles to occupy the same position (exclusion dynamics). We show under mild conditions on the tail probabilities of the collision time that the dynamics are related by an explicit exponential martingale change of measure of one another. This generalises a recent result in the integrable probability literature relating TASEP on the ring to asymmetric walkers conditioned to never collide.
Comments13 pages
