Vol. 20, No. 3, 1967

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Equilibrium systems of stable processes

Sidney Charles Port

Vol. 20 (1967), No. 3, 487–500

We investigate several phenomena connected with the movement of particles through a compact subset B of d-dimensional Eucledian space in a system of infinitely many particles in statistical equilibrium, where each particle moves independenlly of the other particles according to the laws of the same symmetric stable process. In particular, we show that the volume of B governs the rate of flow of particles through B, and that on the one hand, for transient processes, the Riesz capacity of B governs the rate at which new particles hit B and at which particles permanently depart from B, while on the other hand, for recurrent processes, the rate at which new particles hit B is independent of B.

Mathematical Subject Classification
Primary: 60.60
Received: 24 March 1966
Published: 1 March 1967
Sidney Charles Port