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Invariant Bipartite random graphs on RPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2014 (English)In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 51, no 3, 769-779 p.Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

2014. Vol. 51, no 3, 769-779 p.
##### Keyword [en]

Poisson process, random graphs, bipartite, stable matching, percolation
##### National Category

Mathematics
##### Research subject

Mathematical Statistics
##### Identifiers

URN: urn:nbn:se:su:diva-106729ISI: 000342035400013OAI: oai:DiVA.org:su-106729DiVA: diva2:738448
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt449",{id:"formSmash:j_idt449",widgetVar:"widget_formSmash_j_idt449",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt456",{id:"formSmash:j_idt456",widgetVar:"widget_formSmash_j_idt456",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt462",{id:"formSmash:j_idt462",widgetVar:"widget_formSmash_j_idt462",multiple:true});
Available from: 2014-08-18 Created: 2014-08-18 Last updated: 2017-12-05Bibliographically approved
##### In thesis

Suppose that red and blue points occur in $\mathbb{R}^d$ according to two simple point processes with finite intensities $\lambda_{\mathcal{R}}$ and $\lambda_{\mathcal{B}}$, respectively. Furthermore, let $\nu$ and $\mu $ be two probability distributions on the strictly positive integers with means $\bar{\nu}$ and $\bar{\mu}$, respectively. Assign independently a random number of stubs (half-edges) to each red (blue) point with law $\nu$ ($\mu$). We are interested in translation-invariant schemes for matching stubs between points of different colors in order to obtain random bipartite graphs in which each point has a prescribed degree distribution with law $\nu$ or $\mu$ depending on its color. For a large class of point processes we show that such translation-invariant schemes matching a.s. all stubs are possible if and only if\[ \lambda_{\mathcal{R}} \bar{\nu}= \lambda_{\mathcal{B}} \bar{\mu}, \]also including the case when $\bar{\nu}=\bar{\mu}=\infty$ so that both sides are infinite. Furthermore, we study a particular scheme based on the Gale-Shapley stable marriage problem. For this scheme we give sufficient conditions on $\nu$ and $\mu$ for the presence and absence of infinite components. These results are two-color versions of those obtained by Deijfen, Holroyd and H\"{a}ggstr\"{o}m.

1. Spatial Marriage Problems and Epidemics$(function(){PrimeFaces.cw("OverlayPanel","overlay739314",{id:"formSmash:j_idt729:0:j_idt733",widgetVar:"overlay739314",target:"formSmash:j_idt729:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1219",{id:"formSmash:lower:j_idt1219",widgetVar:"widget_formSmash_lower_j_idt1219",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1220_j_idt1222",{id:"formSmash:lower:j_idt1220:j_idt1222",widgetVar:"widget_formSmash_lower_j_idt1220_j_idt1222",target:"formSmash:lower:j_idt1220:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});