Electronic Journal of Probability

Perturbation analysis of the van den Berg Kesten inequality for determinantal probability measures

Franz Merkl and Silke Rolles

Full-text: Open access

Abstract

This paper describes a second order perturbation analysis of the BK property in the space of Hermitean determinantal probability measures around the subspace of product measures, showing that the second order Taylor approximation of the BK inequality holds for increasing events.

Article information

Source
Electron. J. Probab., Volume 18 (2013), paper no. 92, 20 pp.

Dates
Accepted: 24 October 2013
First available in Project Euclid: 4 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465064317

Digital Object Identifier
doi:10.1214/EJP.v18-2339

Mathematical Reviews number (MathSciNet)
MR3126575

Zentralblatt MATH identifier
1286.60010

Subjects
Primary: 60C05: Combinatorial probability
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Keywords
BK inequality determinantal probability measure negative association Reimer's inequality

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Merkl, Franz; Rolles, Silke. Perturbation analysis of the van den Berg Kesten inequality for determinantal probability measures. Electron. J. Probab. 18 (2013), paper no. 92, 20 pp. doi:10.1214/EJP.v18-2339. https://projecteuclid.org/euclid.ejp/1465064317


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References

  • Borgs, C.; Chayes, J. T.; Randall, D. The van den Berg-Kesten-Reimer inequality: a review. Perplexing problems in probability, 159-173, Progr. Probab., 44, Birkhäuser Boston, Boston, MA, 1999.
  • Grimmett, G. Percolation. Second edition. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 321. Springer-Verlag, Berlin, 1999. xiv+444 pp. ISBN: 3-540-64902-6
  • Jonasson, J. The BK inequality for pivotal sampling a.k.a. the Srinivasan sampling process, Electron. Comm. Probab. 18 (2013), no. 35, 1-6 (electronic). DOI:10.1214/ECP.v18-2045
  • Lyons, R. Determinantal probability measures. Publ. Math. Inst. Hautes Études Sci. No. 98 (2003), 167-212.
  • Reimer, D. Proof of the van den Berg-Kesten conjecture. Combin. Probab. Comput. 9 (2000), no. 1, 27-32.
  • van den Berg, J.; Fiebig, U. On a combinatorial conjecture concerning disjoint occurrences of events. Ann. Probab. 15 (1987), no. 1, 354-374.
  • van den Berg, J.; Gandolfi, A. BK-type inequalities and generalized random-cluster representations. Probab. Theory Related Fields 157 (2013), no. 1-2, 157-181.
  • van den Berg, J.; Jonasson, J. A BK inequality for randomly drawn subsets of fixed size. Probab. Theory Related Fields 154 (2012), no. 3-4, 835-844.
  • van den Berg, J.; Kesten, H. Inequalities with applications to percolation and reliability. J. Appl. Probab. 22 (1985), no. 3, 556-569.