On the Convergence to the Continuum of Finite Range Lattice Covariances

Abstract

In J. Stat. Phys. 115, 415-449 (2004) Brydges, Guadagni and Mitter proved the existence of multiscale expansions of a class of lattice Green's functions as sums of positive definite finite range functions (called fluctuation covariances). The lattice Green's functions in the class considered are integral kernels of inverses of second order positive self adjoint operators with constant coefficients and fractional powers thereof. The fluctuation coefficients satisfy uniform bounds and the sequence converges in appropriate norms to a smooth, positive definite, finite range continuum function. In this note we prove that the convergence is actually exponentially fast.

14 pages. We have added further references as well as a proof of Corollary 2.2. This version submitted for publication

References in corpus (4)

• Finite range Decomposition of Gaussian Processes
• Kosterlitz-Thouless Transition Line for the Two Dimensional Coulomb Gas
• The Global Renormalization Group Trajectory in a Critical Supersymmetric Field Theory on the Lattice Z^3
• Infinite volume limit for the dipole gas

Cited by in corpus (3)

• Critical exponents for long-range O(n) models below the upper critical dimension
• A simple method for finite range decomposition of quadratic forms and Gaussian fields
• On a Finite Range Decomposition of the Resolvent of a Fractional Power of the Laplacian