A multitype random sequential process. II. Distribution of particle size and vacant space length in the saturation limit

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Abstract
A one-dimensional lattice space of n equivalent compartments is filled sequentially at random with nonoverlapping particles of integral length β ( β-bell particles), the latter assumed to be a random variable with probability distribution { pq,...,pr} on { q,q+1,...,r−1,r}, q≥1. Due to configurational degeneracies the relative probability p*k,n of ultimately finding a k-bell particle on the saturated lattice space will generally not coincide with pk, the ‘‘input’’ probability. In the present paper we shall determine p*k,n, k=q,...,r, and its limit as n tends to infinity. Some more insight into the occupation configuration of the lattice space in the jammed state is gotten by means of the length distribution of stretches of unoccupied compartments (gaps).

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