SISSA Open Science

Asymptotic behavior of the dirichlet energy on poisson point clouds

Show simple item record

dc.contributor.author Braides, andrea
dc.contributor.author Caroccia, Marco
dc.date.accessioned 2022-03-23T09:50:24Z
dc.date.available 2022-03-23T09:50:24Z
dc.date.issued 2022-03-23
dc.identifier.uri http://preprints.sissa.it:8080/xmlui/handle/1963/35442
dc.description SISSA 06/2022/MATE en_US
dc.description.abstract We 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.language.iso en en_US
dc.title Asymptotic behavior of the dirichlet energy on poisson point clouds en_US
dc.type Preprint en_US
dc.contributor.area mathematics en_US


Files in this item

This item appears in the following Collection(s)

Show simple item record

Search SISSA Open Science


Browse

My Account