Ornstein theory

Ornstein-zernike Theory for the Finite Range Ising

Asymptotic theory with hierarchical autocorrelation: Ornstein-Uhlenbeck tree models

Hierarchical autocorrelation in the error term of linear models arises when sampling units are related to each other according to a tree. The residual covariance is parametrized using the tree-distance between sampling units. When observations are modeled using an Ornstein–Uhlenbeck (OU) process along the tree, the autocorrela-tion between two tips decreases exponentially with their tree distan...

ORNSTEIN-ZERNIKE THEORY FOR FINITE RANGE ISING MODELS ABOVE Tc

We derive a precise Ornstein-Zernike asymptotic formula for the decay of the two-point function 〈σ0σx〉β in the general context of finite range Ising type models on Z. The proof relies in an essential way on the a-priori knowledge of the strict exponential decay of the two-point function and, by the sharp characterization of phase transition due to Aizenman, Barsky and Fernández, goes through in...

Rigorous nonperturbative Ornstein-Zernike theory for Ising ferromagnets

– We rigorously derive the Ornstein-Zernike asymptotics of the pair-correlation functions for finite-range Ising ferromagnets in any dimensions and at any temperature above critical. The celebrated heuristic argument by Ornstein and Zernike [1] implies that the asymptotic form of the truncated two-point density correlation function of simple fluids away from the critical region is given by G(~r...

Ornstein - Uhlenbeck Process

Also, a process {Yt : t ≥ 0} is said to have independent increments if, for all t0 < t1 < . . . < tn, the n random variables Yt1 − Yt0 , Yt2 − Yt1 , ..., Ytn − Ytn−1 are independent. This condition implies that {Yt : t ≥ 0} is Markovian, but not conversely. The increments are further said to be stationary if, for any t > s and h > 0, the distribution of Yt+h− Ys+h is the same as the distributio...