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GibbsPointProcess[{"PairPotential",μ, ϕ}, d]
represents a Gibbs point process with density μ and pair-potential function ϕ in .
GibbsPointProcess[{"PairInteraction",μ, h}, d]
represents a Gibbs point process with density μ and pair-interaction function h in .
GibbsPointProcess[{"Papangelou",λ*}, d]
represents a Gibbs point process with Papangelou conditional density in .
GibbsPointProcess[{"Density",f}, d]
represents a Gibbs point process with density function proportional to f in .
Examplesopen allclose all Basic Examples (1)Sample a Poisson point process by GibbsPointProcess with the appropriate density function:
Plot the points over the region:
Scope (4)Simulate a Gibbs point process with density proportional to the number of points:
Use the Markov chain Monte Carlo method to simulate 40 samples over a unit disk:
Compute the average number of points in the region:
Compare to the scaled area of the region:
Sample a Strauss point process by GibbsPointProcess:
Sample the same process by specifying the Papangelou conditional density:
Sample the same process by specifying the pair potential function:
Sample from a hardcore point process with radius 0.3 with respect to a Poisson point process with density :
Compare to the corresponding inhomogeneous Poisson point process simulation:
Simple Gibbs point processes like the StraussHardcorePointProcess have densities that can be expressed solely in terms of the intensity and pair potential , but this is not true in general. A point process that depends on the area of the union of disks around the points has interactions that depend on all possible subsets of points, like the density function below demonstrates:
Define a Gibbs point process with this density:
Simulate a point pattern from the process:
Visualize the points with surrounding disks:
Properties & Relations (1)Compare numbers of points generated with a PoissonPointProcess and a GibbsPointProcess with the appropriate density:
Compute the average number of points in the region for each process simulation:
Compare to the scaled area of the region:
Wolfram Research (2020), GibbsPointProcess, Wolfram Language function, https://reference.wolfram.com/language/ref/GibbsPointProcess.html. TextWolfram Research (2020), GibbsPointProcess, Wolfram Language function, https://reference.wolfram.com/language/ref/GibbsPointProcess.html.
CMSWolfram Language. 2020. "GibbsPointProcess." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/GibbsPointProcess.html.
APAWolfram Language. (2020). GibbsPointProcess. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GibbsPointProcess.html
BibTeX@misc{reference.wolfram_2025_gibbspointprocess, author="Wolfram Research", title="{GibbsPointProcess}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/GibbsPointProcess.html}", note=[Accessed: 12-July-2025 ]}
BibLaTeX@online{reference.wolfram_2025_gibbspointprocess, organization={Wolfram Research}, title={GibbsPointProcess}, year={2020}, url={https://reference.wolfram.com/language/ref/GibbsPointProcess.html}, note=[Accessed: 12-July-2025 ]}
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