PreprintCC BY 4.0HAL
How much do increasing events occur disjointly?
Abstract
We establish two general quantitative lower bounds on the gap in the classical BK inequality for increasing events. The first one is an analogue of Talagrand's quantitative FKG inequality (1996), it is a function of the influences. The second one is specific to the BK inequality, it involves both the influences and the probabilities of symmetric disjoint pivots.
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BibTeX
@misc{tesio2026much,
title = {{How much do increasing events occur disjointly?}},
author = {Pierre Tesio},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32658},
eprint = {2610.32658},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05837398v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - How much do increasing events occur disjointly?
AU - Pierre Tesio
PY - 2026
DA - 2026/10/23
PB - HAL
DO - 10.48550/arxiv.2610.32658
UR - https://hal.science/hal-05837398v1
AB - We establish two general quantitative lower bounds on the gap in the classical BK inequality for increasing events. The first one is an analogue of Talagrand's quantitative FKG inequality (1996), it is a function of the influences. The second one is specific to the BK inequality, it involves both the influences and the probabilities of symmetric disjoint pivots.
ER -