In this paper, we exploit the theory of dense graph limits to provide a new framework to study the stability of graph partitioning methods, which we call structural consistency. Both stability under perturbation as well as asymptotic consistency (i.e., convergence with probability 1 as the sample size goes to infinity under a fixed probability model) follow from our notion of structural consist...

Abstract Existing causal discovery algorithms are often evaluated using two success criteria, one that is typically unachievable and the other which too weak for practical purposes. The criterion—uniform consistency—requires a algorithm identify correct structure at known sample size. but achievable criterion— pointwise only in limit. We investigate intermediate criteria— decidability progressi...

We consider inverse regression models with convolution-type operators which mediate convolution on R (d ≥ 1) and prove a pointwise central limit theorem for spectral regularisation estimators which can be applied to construct pointwise confidence regions. Here, we cope with the unknown bias of such estimators by undersmoothing. Moreover, we prove consistency of the residual bootstrap in this se...

We calculate the off-diagonal density matrix of the homogeneous electron gas at zero temperature using unbiased reptation Monte Carlo calculations for various densities and extrapolate the momentum distribution and the kinetic and potential energies to the thermodynamic limit. Our results on the renormalization factor allow us to validate approximate G0W0 calculations concerning quasiparticle p...

We consider estimation of quantile curves for a general class of nonstationary processes. Consistency and central limit results are obtained for local linear quantile estimates under a mild short-range dependence condition. Our results are applied to environmental data sets. In particular, our results can be used to address the problem of whether climate variability has changed, an important pr...

We propose a new approach to the self-consistency equation, which arises in the problem of the motion of a hole in a quantum antiferromagnet, appropriate to the case of small exchange energy J . The functional equation for the Green function is transformed into a differential equation; its solutions are analyzed and compared to the existing numerical calculations. This method allows one to stud...

Twisted Eguchi-Kawai reduced chiral models are shown to be formally equivalent a U(1) non-commutative parent theory. The non-commutative theory describes the vacuum dynamics of the non-commutative charged tachyonic field of a brane system. To make contact with the continuum non-commutative theory, a double scaling large N limit for the reduced model is required. We show a possible limiting proc...