 97283 Collet P., Eckmann J.P.
 Oscillations of Observables in 1Dimensional Lattice Systems
(203K, Postscript)
May 17, 97

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Abstract. Using, and extending, striking inequalities by V.V. Ivanov on the
downcrossings of monotone functions and ergodic sums, we give
universal bounds on the probability of finding oscillations of
observables in 1dimensional lattice gases in infinite
volume. In particular, we study the finite volume average of the
occupation number as one runs through an
increasing sequence of boxes of size $2n$ centered at the origin.
We show that the probability to see $k$
oscillations of this average between
two values $\beta $ and $0<\alpha <\beta $ is
bounded by $C R^k$, with $R<1$, where the constants
$C$ and $R$ do {\em not} depend on any detail of the
model, nor on the state one observes, but only on the ratio $\alpha/\beta $.
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