Matches in SemOpenAlex for { <https://semopenalex.org/work/W4301967588> ?p ?o ?g. }
Showing items 1 to 58 of
58
with 100 items per page.
- W4301967588 abstract "In this chapter we review some examples, methods, and recent results involving comparison of clustering properties of point processes. Our approach is founded on some basic observations allowing us to consider void probabilities and moment measures as two complementary tools for capturing clustering phenomena in point processes. As might be expected, smaller values of these characteristics indicate less clustering. Also, various global and local functionals of random geometric models driven by point processes admit more or less explicit bounds involving void probabilities and moment measures, thus aiding the study of impact of clustering of the underlying point process. When stronger tools are needed, directional convex ordering of point processes happens to be an appropriate choice, as well as the notion of (positive or negative) association, when comparison to the Poisson point process is considered. We explain the relations between these tools and provide examples of point processes admitting them. Furthermore, we sketch some recent results obtained using the aforementioned comparison tools, regarding percolation and coverage properties of the Boolean model, the SINR model, subgraph counts in random geometric graphs, and more generally, U-statistics of point processes. We also mention some results on Betti numbers for v{C}ech and Vietoris-Rips random complexes generated by stationary point processes. A general observation is that many of the results derived previously for the Poisson point process generalise to some sub-Poisson processes, defined as those clustering less than the Poisson process in the sense of void probabilities and moment measures, negative association or dcx-ordering." @default.
- W4301967588 created "2022-10-06" @default.
- W4301967588 creator A5004098186 @default.
- W4301967588 creator A5028666798 @default.
- W4301967588 date "2014-01-01" @default.
- W4301967588 modified "2023-10-15" @default.
- W4301967588 title "Clustering comparison of point processes with applications to random geometric models" @default.
- W4301967588 hasPublicationYear "2014" @default.
- W4301967588 type Work @default.
- W4301967588 citedByCount "0" @default.
- W4301967588 crossrefType "book-chapter" @default.
- W4301967588 hasAuthorship W4301967588A5004098186 @default.
- W4301967588 hasAuthorship W4301967588A5028666798 @default.
- W4301967588 hasBestOaLocation W43019675882 @default.
- W4301967588 hasConcept C100906024 @default.
- W4301967588 hasConcept C105795698 @default.
- W4301967588 hasConcept C118615104 @default.
- W4301967588 hasConcept C121332964 @default.
- W4301967588 hasConcept C121864883 @default.
- W4301967588 hasConcept C16757284 @default.
- W4301967588 hasConcept C2524010 @default.
- W4301967588 hasConcept C28719098 @default.
- W4301967588 hasConcept C33923547 @default.
- W4301967588 hasConcept C41008148 @default.
- W4301967588 hasConcept C67499762 @default.
- W4301967588 hasConcept C73555534 @default.
- W4301967588 hasConcept C88871306 @default.
- W4301967588 hasConceptScore W4301967588C100906024 @default.
- W4301967588 hasConceptScore W4301967588C105795698 @default.
- W4301967588 hasConceptScore W4301967588C118615104 @default.
- W4301967588 hasConceptScore W4301967588C121332964 @default.
- W4301967588 hasConceptScore W4301967588C121864883 @default.
- W4301967588 hasConceptScore W4301967588C16757284 @default.
- W4301967588 hasConceptScore W4301967588C2524010 @default.
- W4301967588 hasConceptScore W4301967588C28719098 @default.
- W4301967588 hasConceptScore W4301967588C33923547 @default.
- W4301967588 hasConceptScore W4301967588C41008148 @default.
- W4301967588 hasConceptScore W4301967588C67499762 @default.
- W4301967588 hasConceptScore W4301967588C73555534 @default.
- W4301967588 hasConceptScore W4301967588C88871306 @default.
- W4301967588 hasLocation W43019675881 @default.
- W4301967588 hasLocation W43019675882 @default.
- W4301967588 hasLocation W43019675883 @default.
- W4301967588 hasOpenAccess W4301967588 @default.
- W4301967588 hasPrimaryLocation W43019675881 @default.
- W4301967588 hasRelatedWork W2061819184 @default.
- W4301967588 hasRelatedWork W2068352195 @default.
- W4301967588 hasRelatedWork W2093139423 @default.
- W4301967588 hasRelatedWork W2238117203 @default.
- W4301967588 hasRelatedWork W2591746957 @default.
- W4301967588 hasRelatedWork W2755149066 @default.
- W4301967588 hasRelatedWork W3149607936 @default.
- W4301967588 hasRelatedWork W3169048396 @default.
- W4301967588 hasRelatedWork W4233361775 @default.
- W4301967588 hasRelatedWork W4301967588 @default.
- W4301967588 isParatext "false" @default.
- W4301967588 isRetracted "false" @default.
- W4301967588 workType "book-chapter" @default.