Random point processes

Random Sampling of Random Processes: Stationary Point Processes

This is the first of a series of papers treating randomly sampled random processes. Spectral analysis of the resulting samples presupposes knowledge of the statistics of 1 t~}, the random point process whose variates represent the sampling times. We introduce a class of s ta t ionary point processes, whose s ta t ionar i ty (as characterized by any of several equivalent criteria) leads to wide-...

Random Functions and Point Processes

Random Partitioning Problems Involving Poisson Point Processes On The Interval

Suppose some random resource (energy, mass or space) χ ≥ 0 is to be shared at random between (possibly infinitely many) species (atoms or fragments). Assume Eχ = θ < ∞ and suppose the amount of the individual share is necessarily bounded from above by 1. This random partitioning model can naturally be identified with the study of infinitely divisible random variables with Lévy measure concentra...

Large Deviation Principle for Non-Interacting Boson Random Point Processes

Limit theorems, including the large deviation principle, are established for random point processes (fields), which describe the position distributions of the perfect boson gas in the regime of the Bose-Einstein condensation. We compare these results with those for the case of the normal phase.

Statistics of Extreme Spacings in Determinantal Random Point Processes

We study determinantal translation-invariant random point processes on the real line. Under some technical assumptions on the correlation kernel, we prove that the smallest nearest spacings in a large interval have Poisson statistics as the length of the interval goes to infinity. 2000 Math. Subj. Class. 60G55, 60G70.