Conditional intensity and gibbsianness of determinantal point processes

Journal of Statistical Physics

Volumn 118, Issue 1-2, 2005, Pages 55-84

  Georgii, Hans Otto ^a   Yoo, Hyun Jae ^b  

^a UNIVERSITY OF MUNICH   (Germany)

^b Yonsei University College of Dentistry   (South Korea)

Author keywords

Determinantal point process; Fermion point process; Gibbs point process; Papangelou intensity; Percolation; Stochastic domination

Indexed keywords

EID: 84958757954     PISSN: 00224715     EISSN: 15729613     Source Type: Journal    
DOI: 10.1007/s10955-004-8777-5     Document Type: Article

References (32)

1. R. Bhatia, Matrix Analysis (Springer, New York, 1997).
2. A. Borodin, A. Okounkov, and G. Olshanski, Asymptotics of Plancherel measures for symmetric groups, J. Am. Math. Soc. 13(3), 481-515 (2000).
3. A. Borodin and G. Olshanski, Point processes and the infinite symmetric group, Part VI: Summary of results, available online at URL http://arxiv.org/abs/math.RT/9810015.
4. D. J. Daley and D. Vere-Jones, An Introduction to the Theory of Point Processes (Springer-Verlag, New York, 1988).
5. H.-O. Georgii and T. Küneth, Stochastic comparison of point random fields, J. Appl. Prob. 34:868-881 (1997).
6. E. Glötzl, Konstruktion der bedingten Energie eines Punktprozesses, Serdica 7:217-233 (1981).
7. G. Grimmett, Percolation, 2nd ed. (Springer, Berlin, 1999).
8. P. R. Halmos and V. S. Sunder, Bounded Integral Operators on L2 Spaces (Springer-Verlag, Berlin, 1978).
9. Y. G. Kondratiev and T. Kuna, Correlation functions for Gibbs measures and Ruelle bounds, Methods Funct. Anal. Topology 9:9-58 (2003).
10. O. K. Kozlov, Gibbsian description of point random fields, Theory Prob. Appl. 21:339-355 (1976).
11. R. Lyons, Determinantal probability measures, Publ. Math. Inst. Hautes Études Sci. 98:167-212 (2003).
12. R. Lyons and J. E. Steif, Stationary determinantal process: Phase multiplicity, Bernoullicity, entropy, and domination, Duke Math. J. 120(3), 515-575 (2003).
13. O. Macchi, The coincidence approach to stochastic point processes, Adv. Appl. Prob. 7:83-122 (1975).
14. K. Matthes, W. Warmuth, J. Mecke, Bemerkungen zu einer Arbeit von Nguyen Xuan Xanh und Hans Zessin, Math. Nachr. 88:117-127 (1979).
15. J. Mecke, Stationäre zufällige Maße auf lokalkompakten abelschen Gruppen, Z. Wahrscheinlichkeitstheorie verw. Geb. 9:36-58 (1967).
16. R. Meester and R. Roy, Continuum Percolation (Cambridge University Press, 1996).
17. X. X. Nguyen and H. Zessin, Integral and differential characterizations of the Gibbs process, Math. Nachr. 88:105-115 (1979).
18. M. Ohya and D. Petz, Quantum Entropy and its Use (Springer-Verlag, Berlin, 1993).
19. F. Papangelou, The conditional intensity of general point processes and an application to line processes, Z. Wahrscheinlichkeitstheorie verw. Geb. 28:207-226 (1974).
20. C. J. Preston, Spatial birth-and-death processes, Bull. Inst. Int. Statist. 46:371-391 (1976).
21. C. J. Preston, Random Fields, Lecture Notes in Mathematics Vol. 534 (Springer Verlag, Berlin, 1976).
22. M. Reed and B. Simon, Methods of Modern Mathematical Physics II: Fourier Analysis, Self-Adjointness (Academic Press, New York, 1975).
23. H. Shimomura, Poisson measures on the configuration space and unitary representations of the group of diffeomorphisms, J. Math. Kyoto Univ. 34(3), 599-614 (1994).
24. T. Shirai and Y. Takahashi, Random point field associated with certain Fredholm determinant I: fermion, poisson, and boson point processes, J. Funct. Anal. 205:414-463 (2003).
25. T. Shirai and Y. Takahashi, Random point field associated with certain Fredholm determinant II: fermion shift and its ergodic and Gibbs properties, Ann. Prob. 31:1533-1564 (2003).
26. T. Shirai and H. J. Yoo, Glauber dynamics for fermion point processes, Nagoya Math. J. 168:139-166 (2002).
27. B. Simon, Trace Ideals and Their Applications (Cambridge University Press, Cambridge, 1979).
28. A. Soshnikov, Determinantal random point fields, Russ. Math. Surv. 55:923-975 (2000).
29. H. Spohn, Interacting brownian particles: A study of Dyson’s model, in, Hydrodynamic behaviour and interacting particle systems (Minneapolis, Minn., 1986), G. Papanicolaou, ed., IMA Vol. Math. Appl. 9 (1987).
30. H. Spohn, Tracer dynamics in Dyson’s model of interacting brownian particles, J. Stat. Phys. 47:669-679 (1987).
31. V. Strassen, The existence of probability measures with given marginals, Ann. Math. Statist. 36:423-439 (1965).
32. H. J. Yoo, Gibbsianness of fermion random point fields, Preprint (2003).