Global Monte Carlo for fermions using ordered statistics

The standard method for stochastic representation of the fermion determinant is the pseudofermion method [1]. It allows to trade the computation of the determinant in favour of extra noise in the path integral of lattice QCD. The other alternative is to use the stochastic Taylor expansion of [2]. This suffers from the so called probability sign problem which is created by the noise [3]. The problem is less apparent if the method is applied to a fractional power of the determinant, a fact which is used by the Kentucky Monte Carlo algorithm [4]. In this talk I show that the sign problem created by the noise can be eliminated altogether if one uses a certain statistic from a sample of unbiased noisy estimators of the effective fermion action. As expected, a statistics which is an unbiased estimation of the effective fermion action cannot yield an unbiased estimation of the fermion determinant. The opposite logic suggests that a biased estimation of the former could lead in principle to an unbiased estimation of the latter if this is done ”correctly”. This is indeed the case if one chooses a certain order statistic from the sample. I show below how this can be realized using the central limit theorem and the asymptotic distribution of a central order statistic.