CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt166",{id:"formSmash:upper:j_idt166",widgetVar:"widget_formSmash_upper_j_idt166",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt167_j_idt170",{id:"formSmash:upper:j_idt167:j_idt170",widgetVar:"widget_formSmash_upper_j_idt167_j_idt170",target:"formSmash:upper:j_idt167:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

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});
function selectAll()
{
var panelSome = $(PrimeFaces.escapeClientId("formSmash:some"));
var panelAll = $(PrimeFaces.escapeClientId("formSmash:all"));
panelAll.toggle();
toggleList(panelSome.get(0).childNodes, panelAll);
toggleList(panelAll.get(0).childNodes, panelAll);
}
/*Toggling the list of authorPanel nodes according to the toggling of the closeable second panel */
function toggleList(childList, panel)
{
var panelWasOpen = (panel.get(0).style.display == 'none');
// console.log('panel was open ' + panelWasOpen);
for (var c = 0; c < childList.length; c++) {
if (childList[c].classList.contains('authorPanel')) {
clickNode(panelWasOpen, childList[c]);
}
}
}
/*nodes have styleClass ui-corner-top if they are expanded and ui-corner-all if they are collapsed */
function clickNode(collapse, child)
{
if (collapse && child.classList.contains('ui-corner-top')) {
// console.log('collapse');
child.click();
}
if (!collapse && child.classList.contains('ui-corner-all')) {
// console.log('expand');
child.click();
}
}
2014 (English)In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 51, no 3, p. 769-779Article in journal (Refereed) Published
##### Abstract [en]

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

2014. Vol. 51, no 3, p. 769-779
##### Keywords [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, id: diva2:738448
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt486",{id:"formSmash:j_idt486",widgetVar:"widget_formSmash_j_idt486",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt492",{id:"formSmash:j_idt492",widgetVar:"widget_formSmash_j_idt492",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt498",{id:"formSmash:j_idt498",widgetVar:"widget_formSmash_j_idt498",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_idt789:0:j_idt793",widgetVar:"overlay739314",target:"formSmash:j_idt789:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

urn-nbn$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_j_idt1258",{id:"formSmash:j_idt1258",widgetVar:"widget_formSmash_j_idt1258",showEffect:"fade",hideEffect:"fade",showDelay:500,hideDelay:300,target:"formSmash:altmetricDiv"});});

CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1316",{id:"formSmash:lower:j_idt1316",widgetVar:"widget_formSmash_lower_j_idt1316",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1317_j_idt1319",{id:"formSmash:lower:j_idt1317:j_idt1319",widgetVar:"widget_formSmash_lower_j_idt1317_j_idt1319",target:"formSmash:lower:j_idt1317:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});