Abstract
As in the three-dimensional case, we show, from the BBGKY hierarchy and under exponential clustering assumption, that the two-dimensional one-component plasma obeys the compressibility sum rule which links the compressibility to the fourth moment of the two-point correlation function. A new sum rule, which expresses a set of three point-integrals in terms of two-point integrals, is proved. This sum is specific to the two-dimensional case. Finally the problem concerning the definition of the energy density is also examined.
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