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Göteborgs universitets publikationer

A BK inequality for randomly drawn subset of fixed size

Författare och institution:
Jacob van den Berg (-); Johan Jonasson (Institutionen för matematiska vetenskaper, matematik, Chalmers/GU)
Publicerad i:
Probability Theory and Related Fields, 154 ( 3-4 ) s. 835-844
Artikel, refereegranskad vetenskaplig
Sammanfattning (abstract):
The BK inequality (van den Berg and Kesten in J Appl Probab 22:556–569, 1985) says that, for product measures on {0, 1} n , the probability that two increasing events A and B ‘occur disjointly’ is at most the product of the two individual probabilities. The conjecture in van den Berg and Kesten (1985) that this holds for all events was proved by Reimer (Combin Probab Comput 9:27–32, 2000). Several other problems in this area remained open. For instance, although it is easy to see that non-product measures cannot satisfy the above inequality for all events, there are several such measures which, intuitively, should satisfy the inequality for all increasing events. One of the most natural candidates is the measure assigning equal probabilities to all configurations with exactly k 1’s (and probability 0 to all other configurations). The main contribution of this paper is a proof for these measures. We also point out how our result extends to weighted versions of these measures, and to products of such measures.
Ämne (baseras på Högskoleverkets indelning av forskningsämnen):
Matematik ->
Sannolikhetsteori och statistik ->
Matematisk statistik
BK inequality, negative dependence
Chalmers styrkeområden:
Informations- och kommunikationsteknik
Chalmers fundament:
Grundläggande vetenskaper
Postens nummer:
Posten skapad:
2011-12-06 10:59
Posten ändrad:
2016-08-19 10:18

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