= Sharp threshold
For a sequence of nontrivial <increasing events> on finite <product measures>, write $p_x$ for the parameter at which the success probability is $x$. An additive sharp threshold means that $p_{1-\varepsilon}-p_\varepsilon\to0$ for every fixed $0<\varepsilon<1/2$. When the threshold parameter itself tends to zero, relative sharpness instead compares this window with $p_{1/2}$; additive sharpness alone is then a weaker assertion. The <Friedgut-Kalai sharp threshold theorem> provides an explicit additive bound for <transitive increasing events>.
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