Canonical supermartingale couplings

Canonical solution of classical magnetic models with long-range couplings

We study the canonical solution of a family of classical n − vector spin models on a generic d-dimensional lattice; the couplings between two spins decay as the inverse of their distance raised to the power α, with α < d. The control of the thermodynamic limit requires the introduction of a rescaling factor in the potential energy, which makes the model extensive but not additive. A detailed an...

Supermartingale Decomposition with a General Index Set

By Doob’s theorem, supermartingales indexed by the natural numbers decompose into the difference of a uniformly integrable martingale and an increasing process. The relative ease of working with increasing processes rather than supermartingales explains the prominent role of this result in stochastic analysis and in the theory of stochastic integration. Meyer [19] then proved that, under the us...

Loose Couplings

A supermartingale approach to Gaussian process based sequential design of experiments

Gaussian process (GP) models have become a well-established framework for the adaptive design of costly experiments, and in particular, but not only, of computer experiments. GP-based sequential designs have been proposed for various objectives, such as global optimization (estimating the global maximum or maximizer(s) of a function), reliability analysis (estimating a probability of failure) o...

Tau Electroweak Couplings

We review world-average measurements of the tau lepton electroweak couplings, in both decay (including Michel parameters) and in production (Z → ττ and W → τ−ντ ). We review the searches for anomalous weak and EM dipole couplings. Finally, we present the status of several other tau lepton studies: searches for lepton flavor violating decays, neutrino oscillations, and tau neutrino mass limits.