# Moments of $k$-hop counts in the random-connection model

## TL;DR

This paper derives moment identities for multiparameter stochastic integrals in a random-connection model, simplifying the calculation of moments for k-hop counts and advancing theoretical understanding of such models.

## Contribution

It introduces new moment identities for multiparameter processes in a random-connection model, reducing complexity in deriving moments of k-hop counts.

## Key findings

- Derived general moment identities for multiparameter processes.
- Simplified the derivation of moments for k-hop counts.
- Provided a unified framework for moment calculations in the model.

## Abstract

We derive moment identities for the stochastic integrals of multiparameter processes in a random-connection model based on a point process admitting a Papangelou intensity. Those identities are written using sums over partitions, and they reduce to sums over non-flat partition diagrams in case the multiparameter processes vanish on diagonals. As an application, we obtain general identities for the moments of $k$-hop counts in the random-connection model, which simplify the derivations available in the literature.