The DOI matches its Crossref record; 17 of the 17 references it cites were found in a registry or an index.
Determinantal Processes and Independence
Open accessAbstract
We give a probabilistic introduction to determinantal and permanental point processes. Determinantal processes arise in physics (fermions, eigenvalues of random matrices) and in combinatorics (nonintersecting paths, random spanning trees). They have the striking property that the number of points in a region D is a sum of independent Bernoulli random variables, with parameters which are eigenvalues of the relevant operator on L2(D). Moreover, any determinantal process can be represented as a mixture of determinantal projection processes. We give a simple explanation for these known facts, and establish analogous representations for permanental processes, with geometric variables replacing the Bernoulli variables. These representations lead to simple proofs of existence criteria and central limit theorems, and unify known results on the distribution of absolute values in certain processes with radially symmetric distributions.
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Cites
An Introduction to the Theory of Point Processes
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Stochastic geometry and random graphs for the analysis and design of wireless networks
Haenggi, M., Andrews, J. G., Baccelli, F., Dousse, O., & Franceschetti, M. (2009) · IEEE Journal on Selected Areas in Communications · doi:10.1109/jsac.2009.090902 · Cited by 1,719
Torquato, S. (2018) · Physics Reports · doi:10.1016/j.physrep.2018.03.001 · Cited by 499
Zeros of Gaussian Analytic Functions and Determinantal Point Processes
Hough, J., Krishnapur, M., Peres, Y., & Virág, B. (2009) · University Lecture Series · doi:10.1090/ulect/051 · Cited by 496
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Metadata
- Authors
- Hough, J. B., Krishnapur, M., Peres, Y., & Virág, B.
- Venue
- Probability Surveys
- Publisher
- Institute of Mathematical Statistics
- Published
- 2006-01-01
- Volume
- 3
- Issue
- none
- Pages
- 206-229
- ISSN
- 1549-5787 (ISSN-L)
- OpenAlex
- W1958800402
- Cited by
- 494
- References
- 17
- FWCI
- 18.30
- Type
- journal article
- Language
- en
- Open access
- gold
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