Changsoo Bahn, Yong Moon Park and Hyun Jae Yoo
Nonequilibrium Dynamics of Infinite Particle Systems with Infinite Range 
Interactions
(318K,  postscript file)

ABSTRACT.  We discuss the existence and uniqueness of non-equilibrium dynamics of 
infinitely many particles interacting via superstable pair interactions 
in one and two dimensions. The interaction is allowed to be of infinite 
range and of singular at the origin. Under suitable regularity conditions 
on the interaction potential, we show that if the potential decreases 
polynomially as the distance between interacting two particles increases, 
then the tempered solution to the system of Hamiltonian equations exists. 
Moreover, if the potential satisfies further that either it has 
 a subexponential 
decreasing rate or it is everywhere two-times continuously 
differentiable, 
 then we show that the tempered solution is unique. The results 
extend those of Dobrushin 
and Fritz obtained for finite range interactions.