Interweaving relations are introduced and studied here in a general Markovian setting as a strengthening of usual intertwining relations between semigroups, obtained by adding a randomized delay feature. They provide a new classification scheme of the set of Markovian semigroups which enables to transfer from a reference semigroup and up to an independent warm-up time, some ergodic, analytical and mixing properties including the $\varphi$-entropy convergence to equilibrium, the hyperboundedness and when the warm-up time is deterministic the cut-off phenomena. We also present several useful transformations that preserve interweaving relations. We provide a variety of examples of interweaving relations ranging from classical, discrete, and non-local Laguerre and Jacobi semigroups to degenerate hypoelliptic Ornstein-Uhlenbeck semigroups and some non-colliding particle systems

中文翻译：

---

关于交织关系

交织关系在这里在一般马尔可夫设置中被引入和研究，作为通过添加随机延迟特征获得的半群之间通常交织关系的加强。它们提供了一组马尔可夫半群的新分类方案，可以从参考半群转移到独立的预热时间，一些遍历的、分析的和混合的属性，包括 $\varphi$-熵收敛到平衡，超界和当预热时间是确定性的截止现象。我们还提出了几个有用的转换，以保持交织关系。我们提供了各种交织关系的例子，从经典的、离散的、