论文标题
连续时间摩尔仪过程
Continuous-time Mallows processes
论文作者
论文摘要
在本文中，我们介绍了\ textit {mallows process}，定义为具有分布式边缘的摩洛斯的连续时间càdlàg进程。我们表明存在这样的过程，并且可以局限于具有某些自然特性。特别是，我们证明存在\ textIt {常规} mallows流程，定义为其反转数$ \ mathrm {inv} _j（σ）= | \ {i \ in [j-1]：σ（I）>σ（i）>σ（i）>σ（j）\} | $是独立的稳定进程的specoChastic流程。我们进一步表明，存在一个独特的马尔可夫进程，这是一个常规的摩洛哥手术过程。最后，我们研究了常规木棍过程的特性，并在这些物体的结构上显示了各种结果。除其他外，我们证明了与常规木匠过程相关的图形结构看起来像\ textit {Expanded hypercube}，在该dimension $ k \ in [n] $中，我们将$ k $ hyperipubes堆叠在一起；我们还证明，常规木匠过程的第一个跳跃时间会融合到泊松点过程中。
In this article, we introduce \textit{Mallows processes}, defined to be continuous-time càdlàg processes with Mallows distributed marginals. We show that such processes exist and that they can be restricted to have certain natural properties. In particular, we prove that there exists \textit{regular} Mallows processes, defined to have their inversions numbers $\mathrm{Inv}_j(σ)=|\{i\in[j-1]:σ(i)>σ(j)\}|$ be independent increasing stochastic processes with jumps of size $1$. We further show that there exists a unique Markov process which is a regular Mallows process. Finally, we study properties of regular Mallows processes and show various results on the structure of these objects. Among others, we prove that the graph structure related to regular Mallows processes looks like an \textit{expanded hypercube} where we stacked $k$ hypercubes on the dimension $k\in[n]$; we also prove that the first jumping times of regular Mallows processes converge to a Poisson point process.
