MPEJ Volume 1, No.1, 12pp
Received: March 23, 1995, Revised: May 3, 1995, Accepted: May 3, 1995

Giovanni Gallavotti
Reversible Anosov diffeomorphisms and large deviations.

ABSTRACT:  the volume contraction obeys a large deviation rule

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MPEJ Volume 1, No.2, 37pp
Received: June 17, 1995, Accepted: July 10, 1995

Adam W. Majewski, Boguslaw Zegarlinski
Quantum Stochastic Dynamics I

ABSTRACT:  In the context of non-commutative $\BL_p$ spaces
we discuss the conditions for existence and ergodicity
of translation invariant stochastic spin flip and diffusion dynamics
for quantum spin systems with finite range interactions on a lattice.

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MPEJ Volume 1, No.3, 28pp
Received: September 8, 1995, Revised: October 16, 1995, Accepted: October 23, 1995

Jacques Magnen, Vincent Rivasseau
A Single Scale Infinite Volume Expansion
for Three Dimensional Many Fermion Green's Functions

ABSTRACT:  In [FMRT1] we introduced a cluster expansion for many Fermion
systems in two space dimensions based on a so-called sector decomposition.
In this paper a completely different expansion is introduced to treat
the more difficult case of three (or more) space dimensions: it is based
on an auxiliary scale decomposition and the use of the Hadamard inequality.
We prove that the perturbative expansion for a single scale model has a
convergence radius independent of the scale. This is a typical result,
proved in the two dimensional case in [FMRT1], which we cannot obtain
in three dimensions by naive extrapolation of the sector method.
Although we do not treat in this paper the full (multiscale) system, 
we hope this new method to be a significant step towards the rigorous
construction of the BCS theory of superconductivity in three space dimensions. 

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MPEJ Volume 1, No.4, 35pp
Received: August 25, 1995, Revised: November 16, 1995, Accepted: November 22, 1995

Gregory F. Lawler
Nonintersecting Planar Brownian Motions

ABSTRACT:  In this paper we construct a measure on pairs of Brownian motions
starting at the same point conditioned so their paths do not intersect.
The construction of this measure is a start towards the rigorous
understanding of nonintersecting Brownian motions as a conformal field.
Let $B^1,B^2$ be independent Brownian motions in $\R^2$
starting at distinct points on the unit circle.
Let $T_r^j$ be the first time
that the $j$th Brownian motion reaches distance $r$
and let $D_r$ be the event
$$  D_r = \{B^1[0,T_{e^r}^1] \cap B^2[0,T_{e^r}^2] = \emptyset \} . $$
We construct the measure by considering the limit
of the measure induced by Brownian motions conditioned on the event $D_r$. 

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MPEJ Volume 1, No.5, 13pp
Received: March 24, 1995, Revised: September 11, 1995, Accepted: September 29, 1995

G. Gallavotti, G. Gentile, V. Mastropietro
Field theory and KAM tori

ABSTRACT:  The parametric equations of KAM tori for an l degrees of freedom
quasi integrable system, are shown to be one point Schwinger functions
of a suitable euclidean quantum field theory on the l dimensional torus.
The KAM theorem is equivalent to an ultraviolet stability theorem.
A renormalization group treatment of the field theory leads to a resummation
of the formal perturbation series and to an expansion in terms of
$l^2$ new parameters forming a $l\times l$ matrix $\sigma_\epsilon$
(identified as a family of renormalization constants).
The matrix $\sigma_\epsilon$ is an analytic function of the coupling $\epsilon$
at small $\epsilon$: the breakdown of the tori at large $\epsilon$
is speculated to be related to the crossing by $\sigma_\epsilon$ of a
"critical" surface at a value $\epsilon=\epsilon_c$ where the function
$\sigma_epsilon$ is still finite. A mechanism for the possible universality
of the singularities of parametric equations for the invariant tori,
in their parameter dependence as well as in the $\epsilon_c-\epsilon$ dependence,
is proposed.

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MPEJ Volume 1, No.6, 24pp
Received: October 5, 1995, Revised: November 30, 1995, Accepted: December 6, 1995

Hans Koch, Peter Wittwer
Bounds on the Zeros of a Renormalization Group Fixed Point

ABSTRACT:  We prove that the Renormalization Group transformation
for the Laplace transform of the d=3 Dyson-Baker hierarchical model
has a nontrivial entire analytic fixed point whose zeros all lie
on the imaginary axis. Sharp upper and lower bounds on 80 of these zeros
are used to verify the assumptions made in reference [11].
Our proof is computer-assisted.