论文标题
周期性麦克唐纳过程的自由田间理论和可观察
Free field theory and observables of periodic Macdonald processes
论文作者
论文摘要
我们建议定期的麦克唐纳流程作为$（q，t）$ - 定期舒尔过程的变形和麦克唐纳流程的定期类似物。众所周知，在与对称函数家族有关的随机过程理论中，类似凯奇的身份给出了分区函数的明确表达。我们计算依赖于麦克唐纳理论的自由领域实现的定期麦克唐纳过程的分区函数。我们还研究了几个可观察到的家族，以定期进行麦克唐纳过程，并提供其时刻的公式。技术工具是由MacDonald对称函数对角线的运算符的自由场实现，其中操作员通过顶点操作员允许表达式。我们表明，当我们采用Plancherel专业知识时，相应的周期性麦克唐纳过程与年轻图值的周期性连续过程有关。众所周知，对于周期性的Schur过程，只有在我们扩展时才考虑到收费时，才能使用确定性公式。我们还考虑了这种转变的周期性麦克唐纳过程，并讨论了他们的schur限制。
We propose periodic Macdonald processes as a $(q,t)$-deformation of periodic Schur processes and a periodic analogue of Macdonald processes. It is known that, in the theory of stochastic processes related to a family of symmetric functions, the Cauchy-like identity gives an explicit expression of a partition function. We compute the partition functions of periodic Macdonald processes relying on the free field realization of the Macdonald theory. We also study several families of observables for periodic Macdonald processes and give formulas of their moments. The technical tool is the free field realization of operators that are diagonalized by the Macdonald symmetric functions, where the operators admit expressions by means of vertex operators. We show that, when we adopt Plancherel specializations, the corresponding periodic Macdonald process is related to a Young diagram-valued periodic continuous process. It is known that, for periodic Schur processes, determinantal formulas are only available when we extend them to take into account the charge. We also consider this kind of shift-mixed periodic Macdonald processes and discuss their Schur-limit.
