论文标题
rudvalis卡片的缩放限制
Scaling limits for Rudvalis card shuffles
论文作者
论文摘要
我们考虑了DiaConis和Saloff-Coste在\ cite {对称性}中引入的Rudvalis Card Shuffle及其一些变化，我们将它们投影到某些随机相互作用的粒子系统。对于后者，我们得出了流体动力学限制，并研究了平衡波动。我们的结果表明，对于这些洗牌，当我们考虑鲁德瓦利斯洗牌的不对称变化时，欧拉尔量表中的流体动力极限是根据传输方程式给出的，其常数取决于系统的汇率。对于这种洗牌的对称和弱的不对称变化，在扩散的时间尺度上，进化是通过martingale问题的解决方案给出的。
We consider the Rudvalis card shuffle and some of its variations that were introduced by Diaconis and Saloff-Coste in \cite{symmetrized}, and we project them to some stochastic interacting particle system. For the latter, we derive the hydrodynamic limits and we study the equilibrium fluctuations. Our results show that, for these shuffles, when we consider an asymmetric variation of the Rudvalis shuffle, the hydrodynamic limit in Eulerian scale is given in terms of a transport equation with a constant that depends on the exchange rates of the system; while for symmetric and weakly asymmetric variations of this shuffle, in diffusive time scale, the evolution is given by the solution of a martingale problem.
