## The Annals of Probability

- Ann. Probab.
- Volume 3, Number 4 (1975), 597-607.

### On a Problem of Cox Concerning Point Processes in $R^k$ of "Controlled Variability"

#### Abstract

Suppose that the $k$-dimensional lattice points are displaced independently of each other with the same probability distribution. Denote by $\operatorname{Var} N(A)$ the variance of the number of displaced points contained in the set $A$. The asymptotic behaviour of $\operatorname{Var} N(A)$ is determined for large convex $A$'s.

#### Article information

**Source**

Ann. Probab. Volume 3, Number 4 (1975), 597-607.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aop/1176996303

**Digital Object Identifier**

doi:10.1214/aop/1176996303

**Mathematical Reviews number (MathSciNet)**

MR388536

**Zentralblatt MATH identifier**

0316.60037

**JSTOR**

links.jstor.org

**Subjects**

Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]

Secondary: 60K99: None of the above, but in this section

**Keywords**

Stochastic point processes random displacements geometrical probability

#### Citation

Gacs, P.; Szasz, D. On a Problem of Cox Concerning Point Processes in $R^k$ of "Controlled Variability". Ann. Probab. 3 (1975), no. 4, 597--607. doi:10.1214/aop/1176996303. https://projecteuclid.org/euclid.aop/1176996303