zbMATH — the first resource for mathematics

Threshold phenomena on product spaces: BKKKL revisited (once more). (English) Zbl 1189.60071
Summary: We revisit the work of J. Bourgain, J. Kahn, G. Kalai, Y. Katznelson and N. Linial [Isr. J. Math. 77, No. 1–2, 55-64(1992; Zbl 0771.60002)] – referred to as “BKKKL” in the title – about influences on Boolean functions in order to give a precise statement of threshold phenomenon on the product space \({1,\dots ,r}^{N}\), generalizing one of the main results of M. Talagrand [Ann. Probab. 22, No. 3, 1576–1587 (1994; Zbl 0819.28002)].

60F20 Zero-one laws
28A35 Measures and integrals in product spaces
60E15 Inequalities; stochastic orderings
Full Text: DOI arXiv EuDML EMIS