论文标题
PFAFFIAN点工艺来自Frem Fermion代数：完美和有条件的措施
Pfaffian Point Processes from Free Fermion Algebras: Perfectness and Conditional Measures
论文作者
论文摘要
确定点过程（DPP）和自由费米克计算之间的类比是众所周知的。我们指出，从自由费米尼代数的角度来看，PFAFFIAN点过程（PFPPS）自然出现，并表明具有附加结构的“加倍”单粒子空间的正收缩定义了独特的PFPP。最近，奥尔尚斯基（Olshanski）颠倒了从自由费米斯（Fermions）到DPPS的方向，提出了一种从准不变概率度量构建费米子状态的方案，并引入了概率度量的完美概念。我们提出了一种检查完美的方法，并表明Schur度量是完美的，只要它们在对称组的作用下是准不变的。我们还研究了与投影算子相关的PFPP的条件措施。因此，我们表明条件度量再次与投影算子相关联的PFPP明确描述了子空间。
The analogy between determinantal point processes (DPPs) and free fermionic calculi is well-known. We point out that, from the perspective of free fermionic algebras, Pfaffian point processes (PfPPs) naturally emerge, and show that a positive contraction acting on a "doubled" one-particle space with an additional structure defines a unique PfPP. Recently, Olshanski inverted the direction from free fermions to DPPs, proposed a scheme to construct a fermionic state from a quasi-invariant probability measure, and introduced the notion of perfectness of a probability measure. We propose a method to check the perfectness and show that Schur measures are perfect as long as they are quasi-invariant under the action of the symmetric group. We also study conditional measures for PfPPs associated with projection operators. Consequently, we show that the conditional measures are again PfPPs associated with projection operators onto subspaces explicitly described.
