We study the Fleming–Viot particle process formed by $N$ interacting continuous-time asymmetric random walks on the cycle graph, with uniform killing. We show that this model has a remarkable exact solvability, despite the fact that it is non-reversible with non-explicit invariant distribution. Our main results include quantitative propagation of chaos and exponential ergodicity with explicit constants, as well as formulas for covariances at equilibrium in terms of the Chebyshev polynomials. We also obtain a bound uniform in time for the convergence of the proportion of particles in each state when the number of particles goes to infinity.

中文翻译：

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循环图中Fleming–Viot型粒子系统的动力学

我们研究了由 $ñ$相互作用的连续时间非对称随机游动在周期图上具有均匀的杀灭力。我们表明，尽管该模型不可逆且具有非显式不变分布，但它具有显着的精确可解性。我们的主要结果包括使用明确常数对混沌和指数遍历进行定量传播，以及根据Chebyshev多项式在平衡时的协方差公式。当粒子数达到无穷大时，我们还获得了时间上有约束的均匀性，以收敛每种状态下粒子的比例。