Factor Point Processes
Jointly with S. Mellick, A. Khezeli solved the problem of the existence of factor point processes in the paper
- A. Khezeli and S. Mellick. On the existence of balancing allocations and factor point processes. arXiv preprint arXiv:2303.05137. 2023. https://doi.org/10.48550/arXiv.2303.05137
Palm Theory on Unimodular Spaces
A. Khezeli proposed a general approach for the construction of point processes on unimodular spaces in
- A. Khezeli. ‘Unimodular Random Measured Metric Spaces and Palm Theory on Them.’ arXiv preprint arXiv:2304.02863. 2023. https://doi.org/10.48550/arXiv.2304.02863
Book Preprint
This book preprint Random Measures, Point Processes, and Stochastic Geometry by François Baccelli, Bartlomiej Blaszczyszyn, and Mohamed Kadhem Karray was posted in January 2020. This book is centered on the mathematical analysis of random structures embedded in the Euclidean space or more general topological spaces, with a main focus on random measures, point processes, and stochastic geometry. Such random structures have been known to play a key role in several branches of natural sciences (cosmology, ecology, cell biology) and engineering (material sciences, networks) for several decades. Their use is currently expanding to new fields like data sciences. The book was designed to help researchers finding a direct path from the basic definitions and properties of these mathematical objects to their use in new and concrete stochastic models.
The material is organized as follows. Random measures and point processes are presented first, whereas stochastic geometry is discussed at the end of the book. For point processes and random measures, parametric models are discussed before non-parametric ones. For the stochastic geometry part, the objects of interest are often considered as point processes in the space of random sets of the Euclidean space. We discuss both general processes such as, e.g., particle processes, and parametric ones like, e.g., Poisson Boolean models of Poisson hyperplane processes.
