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#### A strong zero-one law for connectivity in one-dimensional geometric random graphs with non-vanishing densities

(2007)

We consider the geometric random graph where n points are distributed independently on the unit interval [0,1] according to some probability distribution function F. Two nodes communicate with each other if their distance ...

#### On zero-one laws for connectivity in one-dimensional geometric random graphs

(2006)

We consider the geometric random graph where n points are distributed uniformly and independently on the unit interval [0,1]. Using the method of first and second moments, we provide a simple proof of the "zero-one" law ...

#### Very sharp transitions in one-dimensional MANETs

(2005)

We investigate how quickly phase transitions can occur in one-dimensional geometric random graph models of MANETs. In the case of graph connectivity, we show that the transition width behaves like 1/n (when the number n ...

#### Connectivity in one-dimensional geometric random graphs: Poisson approximations, zero-one laws and phase transitions

(2008-10-24)

Consider n points (or nodes) distributed uniformly and independently on the unit interval [0,1]. Two nodes are said to be adjacent if their distance is less than some given threshold value.For the underlying random graph ...

#### On the critical communication range under node placement with vanishing densities

(2007)

We consider the random network where n points are placed independently on the unit interval [0, 1] according to some probability distribution function F. Two nodes communicate with each other if their distance is less than ...