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 |