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Let D, be the diameter of a partition of the interval [0, t] by renewal moments of a standard Poisson process. Then DJln t + 1 for t + co, in probability. Other theorems on diameters are obtained. J...
We csnsider the hereasing sequenm af non-interngetirng monotone decreasing srg prommes Y: (F}, n = 1, 2, . . , (t > 01, whose jump points mver all the points of the h~mogencous rate 1 Poisson proam...
Let $[mathcal{P}]$ be the points of a Poisson process on $RR^d$ and $F$ a probability distribution with support on the non-negative integers. Models are formulated for generating translation invariant...
Let $[mathcal{P}]$ be the points of a Poisson process on $RR^d$ and $F$ a probability distribution with support on the non-negative integers. Models are formulated for generating translation invariant...
The scale-invariant spacings lemma due to Arratia, Barbour and Tavaré establishes the distributional identity of a self-similar Poisson process and the set of spacings between the points of this proce...

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