Let N circles with homogeneous radius r are deployed with Poisson distribution in area A. These circles are connected if there euclidean distance is less than r.what is the probability P that all circles are connected with each other. Now if x circles are removed with probability Pf what is the probability that these circles are still connected.
4
-
2$\begingroup$ Where does this question come from? See mathoverflow.net/howtoask $\endgroup$– Yemon ChoiCommented Jun 11, 2013 at 7:35
-
$\begingroup$ I'm inclined to guess that the first and second occurrences of "connected" in the question mean different things. Specifically, I guess that Anil is defining a graph, with the circles as vertices, in which two are joined by an edge if their distance is $<r$, and then he is asking about the probability that every two of the circles are joined by a path (not necessarily by a single edge). Without that distinction, the last part of the question, about what happens when some of the circles are deleted, makes no sense. $\endgroup$– Andreas BlassCommented Jun 11, 2013 at 14:15
-
$\begingroup$ I also guess that Anil might not have meant "connected if the[ir] euclidean distance is less than $r$". This would amount to saying that the distance betwen the centers of the circles is $<3r$, since the circles have radius $r$. The use of circles instead of just the centers seems to be just complicating the description --- both the criterion for connectedness (in the first sense) and the requirement that the circles are "deployed ... in area A," which boils down to saying that the centers of the circles are at distance at least $r$ from the boundary of $A$. $\endgroup$– Andreas BlassCommented Jun 11, 2013 at 14:20
-
1$\begingroup$ Looks like a duplicate of mathoverflow.net/questions/76153/… $\endgroup$– Brendan McKayCommented Jun 11, 2013 at 15:06
Add a comment
|