We study the convergence to stationarity for random walks on dynamic random digraphs with given degree sequences. The digraphs undergo full regeneration at independent geometrically distributed random time intervals with parameter $\alpha$. Relaxation to stationarity is the result of an interplay of regeneration and mixing on the static digraph. When the number of vertices $n$ tends to infinity and the parameter $\alpha$ tends to zero, we find three scenarios according to whether $\alpha logn$ converges to zero, infinity or to some finite positive value: when the limit is zero, relaxation to stationarity occurs in two separate stages, the first due to mixing on the static digraph, and the second due to regeneration; when the limit is infinite, there is not enough time for the static digraph to mix and the relaxation to stationarity is dictated by the regeneration only; finally, when the limit is a finite positive value we find a mixed behavior interpolating between the two extremes. A crucial ingredient of our analysis is the control of suitable approximations for the unknown stationary distribution.

我们研究具有给定度数序列的动态随机有向图上随机游动的平稳收敛性。有向图在具有参数的独立几何分布随机时间间隔内进行完全再生$\alpha$。平稳性的松弛是静态图上再生和混合相互作用的结果。当顶点数$ñ$ 趋于无穷大，参数 $\alpha$ 趋于零，我们根据是否找到三个方案 $\alpha 日志ñ$收敛到零，无穷大或某个有限的正值：当极限为零时，平稳性的松弛发生在两个单独的阶段，第一阶段是由于静态有向图上的混合，第二阶段是由于再生。当极限无限大时，静态图没有足够的时间混合，静止性的松弛仅由再生决定；最后，当极限是有限的正值时，我们发现在两个极端之间插值的混合行为。我们分析的关键要素是控制未知平稳分布的合适近似值。