Quantum field theory for discrepancies
نویسندگان
چکیده
The concept of discrepancy plays an important rôle in the study of uniformity properties of point sets. For sets of random points, the discrepancy is a random variable. We apply techniques from quantum field theory to translate the problem of calculating the probability density of (quadratic) discrepancies into that of evaluating certain path integrals. Both their perturbative and non-perturbative properties are discussed. [email protected] [email protected]
منابع مشابه
Quantum field theory for discrepancies II: 1/N corrections using fermions
We calculate the 1/N corrections to the probability distributions of quadratic discrepancies for sets of N random points. This is achieved by the introduction of fermionic variables. We give the diagrammatic expansion up to and including the second order in 1/N . For some discrepancies, we give the explicit expansion to first order. [email protected] [email protected] [email protected]...
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تاریخ انتشار 2008