Numerical solution of an integral equation from point process theory
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We propose and analyze methods for the numerical solution of an integral equation which arises in statistical physics and spatial statistics. Instances of this equation include the Mean Field, Poisson-Boltzmann and Emden equations for the density of a molecular gas, and the Poisson saddlepoint approximation for the intensity of a spatial point process. Conditions are established under which the Picard iteration and the under relaxation iteration converge. Numerical validation is included.
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