论文标题
周期图上Fleming-Viot型粒子系统的动力学
Dynamics of a Fleming-Viot type particle system on the cycle graph
论文作者
论文摘要
我们研究了n相互作用的连续时间不对称随机步行在周期图上形成的Fleming-Viot粒子过程，并杀死了均匀的杀戮。我们表明，尽管该模型不可逆转，但该模型具有非可逆的不变分布。我们的主要结果包括用显式常数的定量繁殖和指数性的磨难，以及在Chebyshev多项式方面平衡的协方差公式。当颗粒数量进入无穷大时，我们还可以在每个状态下的粒子比例收敛，从而获得一个结合的统一。
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.
