Time-interval distributions of a random point process in the detection of classical and nonclassical states of light

2003 ◽  
Vol 5 (4) ◽  
pp. 370-375 ◽  
Author(s):  
C Bendjaballah
Keyword(s):  
Point Process ◽  
Random Point ◽  
Time Interval ◽  
Nonclassical States

scholarly journals Random point processes and tilings arising from Gaussian analytic functions

2014 ◽  
Vol 70 (a1) ◽  
pp. C523-C523
Author(s):  
Michael Baake ◽  
Holger Koesters ◽  
Robert Moody
Keyword(s):  
Point Process ◽  
Analytic Functions ◽  
Point Processes ◽  
Logarithmic Potential ◽  
Basins Of Attraction ◽  
Random Point ◽  
Specific Class ◽  
Determinantal Point Processes ◽  
Point Sets ◽  
Gaussian Analytic Functions

Getting a grasp of what aperiodic order really entails is going to require collecting and understanding many diverse examples. Aperiodic crystals are at the top of the largely unknown iceberg beneath. Here we present a recently studied form of random point process in the (complex) plane which arises as the sets of zeros of a specific class of analytic functions given by power series with randomly chosen coefficients: Gaussian analytic functions (GAF). These point sets differ from Poisson processes by having a sort of built in repulsion between points, though the resulting sets almost surely fail both conditions of the Delone property. Remarkably the point sets that arise as the zeros of GAFs determine a random point process which is, in distribution, invariant under rotation and translation. In addition, there is a logarithmic potential function for which the zeros are the attractors, and the resulting basins of attraction produce tilings of the plane by tiles which are, almost surely, all of the same area. We discuss GAFs along with their tilings and diffraction, and as well note briefly their relationship to determinantal point processes, which are also of physical interest.

Random Point Process

1976 ◽  
Vol 27 (3) ◽  
pp. 782-783
Author(s):  
H. O'Brien
Keyword(s):  
Point Process ◽  
Random Point

An insensitivity property of ladder height distributions

1992 ◽  
Vol 29 (03) ◽  
pp. 616-624
Author(s):  
Michael Frenz ◽  
Volker Schmidt
Keyword(s):  
Point Process ◽  
Ruin Probability ◽  
Initial Level ◽  
Marked Point ◽  
Risk Process ◽  
Marked Point Process ◽  
Time Interval ◽  
Finite Time Interval ◽  
Balance Condition ◽  
Ladder Height

This paper considers the undershoot of a general continuous-time risk process with dependent increments under a certain initial level. The increments are given by the locations and amounts of claims which are described by a stationary marked point process. Under a certain balance condition, it is shown that the distribution of the undershoot depends only on the mark distribution and on the intensity of the underlying point process, but not on the form of its distribution. In this way an insensitivity property is extended which has been proved in Björk and Grandell [3] for the ruin probability, i.e. for the probability that after a finite time interval the initial level will be crossed from above.

An insensitivity property of ladder height distributions

1992 ◽  
Vol 29 (3) ◽  
pp. 616-624 ◽  
Author(s):  
Michael Frenz ◽  
Volker Schmidt
Keyword(s):  
Point Process ◽  
Ruin Probability ◽  
Initial Level ◽  
Marked Point ◽  
Risk Process ◽  
Marked Point Process ◽  
Time Interval ◽  
Finite Time Interval ◽  
Balance Condition ◽  
Ladder Height

This paper considers the undershoot of a general continuous-time risk process with dependent increments under a certain initial level. The increments are given by the locations and amounts of claims which are described by a stationary marked point process. Under a certain balance condition, it is shown that the distribution of the undershoot depends only on the mark distribution and on the intensity of the underlying point process, but not on the form of its distribution. In this way an insensitivity property is extended which has been proved in Björk and Grandell [3] for the ruin probability, i.e. for the probability that after a finite time interval the initial level will be crossed from above.

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