|
|
| |
| ON THE DISTRIBUTION OF RANDOM LINES IN THE GENERAL CASE |
| |
Citation： |
Zheng ming.ON THE DISTRIBUTION OF RANDOM LINES IN THE GENERAL CASE[J].Chinese Annals of Mathematics B,1988,9(1):19~26 |
| Page view： 867
Net amount： 684 |
Authors： |
Zheng ming; |
|
|
| Abstract： |
$L$ is a line in a plane through the origin, with an angle $\[\alpha \]$ to the $x$-axis,$\[0 < \alpha < \pi \]$.$M$ is a point process on positive $x$-axis, Through the nth point of $M$ draw a line with a random angle $\[{\theta _n}\]$ to $x$-axis, $\[{\varphi ^ + }\]$ is the set of intersections of those lines with $\[{L^ + }\]$. Let $\[m = EM\]$. If, for every $\[c > 0\]$, then $\[{\varphi ^ + }\]$ is locally finite on $L$, and let $\[\tilde M\]$ be the point process constructed by $\[{\varphi ^ + }\]$ , then $\[E\tilde M\]$ exists. If, for all interval $\[L \subset {L^ + }\]$, $\[\int_0^\infty {r(I,x)M(dx)} = \infty \]$
then $\[{\varphi ^ + }\]$ is dense on $\[{L^ + }\]$. If $L$ is drawn parallel to $x$-axis,. the same results can be got，and this time $\[\tilde M\]$ is a cluster point process with cluster center $M$. |
Keywords： |
|
Classification： |
|
|
|
Download PDF Full-Text
|
|
|
|
