Advanced Search
MyIDEAS: Login to save this paper or follow this series

Functional BRK Inequalities, and their Duals, with Applications


Author Info

  • Larry Goldstein
  • Yosef Rinott


The inequality conjectured by van den Berg and Kesten in [9], and proved by Reimer in [6], states that for A and B events on S, a product of finitely many finite sets, and P any product measure on S,P(A�B) � P(A)P(B), where A�B are the elementary events which lie in both A and B for `disjoint reasons.' This inequality on events is the special case, for indicator functions, of the inequality having the following formulation. Let X be a random vector with n independent components, each in some space Si (such as R d), and set S = � Si. Say that the function f : S � R depends on K � {1,...,n} if f(x) = f(y) whenever x i = y i for all i � K. Then for any given finite or countable collections of non-negative real valued functions {f a} a� A, {g b} b� B on S which depend on K a and L b respectively, E{sup Ka � Lb f a(X) g b(X)} � E{sup f a(X)} E{sup g b(X)}. Related formulations, and functional versions of the dual inequality on events by Kahn, Saks, and Smyth [4], are also considered. Applications include order statistics, assignment problems, and paths in random graphs.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL:
Download Restriction: no

Bibliographic Info

Paper provided by The Center for the Study of Rationality, Hebrew University, Jerusalem in its series Discussion Paper Series with number dp374.

as in new window
Length: 18 pages
Date of creation: Nov 2004
Date of revision:
Publication status: Published in Journal of Theoretical Probability 20, 275-293 (2007)
Handle: RePEc:huj:dispap:dp374

Contact details of provider:
Postal: Feldman Building - Givat Ram - 91904 Jerusalem
Phone: +972-2-6584135
Fax: +972-2-6513681
Web page:
More information through EDIRC

Related research

Keywords: graphs and paths; positive dependence; order statistics;

This paper has been announced in the following NEP Reports:


References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
as in new window
  1. Karlin, Samuel & Rinott, Yosef, 1980. "Classes of orderings of measures and related correlation inequalities. I. Multivariate totally positive distributions," Journal of Multivariate Analysis, Elsevier, vol. 10(4), pages 467-498, December.
Full references (including those not matched with items on IDEAS)



This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.


Access and download statistics


When requesting a correction, please mention this item's handle: RePEc:huj:dispap:dp374. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Ilan Nehama).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.