Asymptotic behavior of the dirichlet energy on poisson point clouds

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dc.contributor.areamathematicsen_US
dc.contributor.authorBraides, Andrea
dc.contributor.authorCaroccia, Marco
dc.date.accessioned2022-03-23T09:50:24Z
dc.date.available2022-03-23T09:50:24Z
dc.date.issued2022-03-23
dc.descriptionSISSA 06/2022/MATEen_US
dc.description.abstractWe prove that quadratic pair interactions for functions defined on planar Poisson clouds and taking into account pairs of sites of distance up to a certain (large-enough) threshold can be almost surely approximated by the multiple of the Dirichlet energy by a deterministic constant. This is achieved by scaling the Poisson cloud and the corresponding energies and computing a compact discrete-to-continuum limit. In order to avoid the effect of exceptional regions of the Poisson cloud, with an accumulation of sites or with ‘disconnected’ sites, a suitable ‘coarse-grained’ notion of convergence of functions defined on scaled Poisson clouds must be given.en_US
dc.identifier.urihttps://openscience.sissa.it/handle/1963/35442
dc.language.isoenen_US
dc.titleAsymptotic behavior of the dirichlet energy on poisson point cloudsen_US
dc.typePreprinten_US
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