From the GNZ identity to a Dyson–Schwinger cumulant hierarchy for point processes
Year: 2026
Type: article
Abstract: The Georgii–Nguyen–Zessin identity induces a functional differential equation for the cumulant generating functional of a point process admitting a Papangelou conditional intensity. In generating-functional form, this equation takes the structure of a Dyson–Schwinger identity. For pairwise Gibbs point processes, the equation closes: insertion of a point acts as a deterministic shift of the source field. This yields a hierarchy for cumulant densities of all orders, expressing cumulants as differences between the original law and the laws induced by point insertion. The formulation is non-perturbative and provides exact recursion relations for cumulants.
Source: Statistics & Probability Letters
Author: Daniel E. Clark
Institution: University of Southampton
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,180
OpenAlex ID: W7162687375