4d215ab7508a3e089af43fb605dd27d1-Supplemental.pdf

Providing a very low critical probabilitypc means that certification occurs when the simulation ends after alarge number of iterationsm. On the other hand, the projection of X onto any other direction orthogonal tog remains normal distributed. For each couple of parameters(N,T)we make1000 runs and count the number of false positive(i.e. the number of times the algorithm wrongfully asserted thatp < pc). Combining the latter proposal withT we obtain again a proposal reversible w.r.t. Step4: Conclusionbyinduction Let l0 be any critical level such thatπ0(h(X) > l0) > 0. We consider the following induction hypothesisatiterationk: Hk On the event, Lk l0, The probability that the two particle systems are equal tends exponentiallyfastto1whent + .