| Abstract: |
Attractiveness is a fundamental tool in the study of interacting particle
systems. For the basic example of simple exclusion, this property is shown
to hold through the basic coupling construction, which proves the existence
of a markovian coupled process
$(\xi_t,zeta_t)_{t\geq 0}$ that satisfies:
(P) for any two initial configurations $\xi_0\leq\zeta_0$
(coordinate-wise),
$\xi_t\leq\zeta_t$ a.s. for all $t\geq 0$.
We generalize this classical result in two ways, in which the basic coupling
construction is not possible: In one part, we consider conservative particle
systems on $\Z^d$ for which, in each transition, $k$ particles can jump
between sites, with $1\leq k$.
In the second part, we consider exclusion systems with interaction.
In both cases, we give necessary and sufficient conditions on the rates
underwhich those systems are attractive, and give some details on
the construction of a markovian coupled process satisfying (P). We also
prove that under such a coupling, the number of discrepancies between the
two copies of the process is decreasing in time.
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