Applied Probability Research

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Various phenomena in physics, chemistry and biology can be modelled by spatial point processes. A spatial point process is a finite or countable set of random points on a space (i.e., a subset of an Euclidean space). Examples encompass Poisson point processes, characterized by independent points where the total count follows a Poisson distribution; Gibbs point processes, defined by a distribution that is absolutely continuous in relation to that of a Poisson point process; and random geometric graphs, depicting nodes as points and connecting edges between those within a specified distance. Applications of such processes include modeling phenomena as diverse as gas atoms in a chamber, tree locations in a forest as well as base stations of a cellular network over a city.