Finite particle systems and infection models

<jats:p>Infinite particle systems on lattices have been extensively studied in recent years. The main questions of interest concern the ergodic and limiting behaviour of these processes, and their relationship with the dimension of the underlying lattice. A comprehensive review is given by Durrett(<jats:bold>6</jats:bold>).</jats:p><jats:p>One of the more tractable of these processes is the voter model introduced by Clifford and Sudbury(<jats:bold>3</jats:bold>) and much studied since, see for example the monograph by Griffeath(<jats:bold>8</jats:bold>), or the papers by Harris(<jats:bold>11</jats:bold>), Holley and Liggett(<jats:bold>13</jats:bold>), Bramson and Griffeath(<jats:bold>1</jats:bold>) and (<jats:bold>2</jats:bold>) or, for a more general approach, Kelly(<jats:bold>16</jats:bold>).</jats:p><jats:p>In this paper we consider the case where the underlying spatial structure is finite and examine the transient behaviour of the voter process and also the infection process introduced by Williams and Bjerknes(<jats:bold>21</jats:bold>).</jats:p>