Determinantal point processes are point processes whose correlation functions are given by determinants of matrices. The entries of these matrices are given by one fixed function of two variables, which is called the kernel of the point process. It is well known that there are different kernels that induce the same correlation functions. We classify all the possible transformations of a kernel that leave the induced correlation functions invariant, restricting to the case of symmetric kernels.

中文翻译：

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行列式点过程的等效对称核

行列式点过程是点过程，其相关函数由矩阵的行列式给出。这些矩阵的条目由两个变量的一个固定函数给出，称为点过程的核。众所周知，有不同的内核会产生相同的相关函数。我们对内核的所有可能变换进行分类，使诱导相关函数保持不变，仅限于对称内核的情况。