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Comment: 39 pages, review article for the conference "Noncommutative harmonic
analysis" in Bedlewo, Poland, 2006. v1-->v2, corrections in Section 5 and
changes in notation
Comment: 42 pages, LaTeX2e, 0 figures; references added, minor changes in the
text, typos corrected
The goal of this paper is to provide estimates leading to a direct proof of
the exponential decay of the n-point correlation functions for certain
unbounded models of Kac type. The methods are based on estimating higher order
derivatives of the solution of the Witten Laplacian equation on one forms
associated with the hamiltonian of the system. We also provide a formula for
the Taylor coefficients of the pressure that is suitable for a direct proof the
analyticity.
Comment: 18 pages 5 figures
Comment: 53 pages, 1 figure. Editorial changes on page 22 ff
We construct a three-parameter deformation of the Hopf algebra $\LDIAG$. This
is the algebra that appears in an expansion in terms of Feynman-like diagrams
of the {\em product formula} in a simplified version of Quantum Field Theory.
This new algebra is a true Hopf deformation which reduces to $\LDIAG$ for some
parameter values and to the algebra of Matrix Quasi-Symmetric Functions
($\MQS$) for others, and thus relates $\LDIAG$ to other Hopf algebras of
contemporary physics. Moreover, there is an onto linear mapping preserving
products from our algebra to the algebra of Euler-Zagier sums.
We prove a Wegner estimate for a large class of multiparticle Anderson
Hamiltonians on the lattice. These estimates will allow us to prove Anderson
localization for such systems. A detailed proof of localization will be given
in a subsequent paper.
