  Many random combinatorial objects have a component structure whose joint
distribution is equal to that of a process of mutually independent random
variables, conditioned on the value of a weighted sum of the variables. It is
interesting to compare the combinatorial structure directly to the independent
discrete process, without renormalizing. The quality of approximation can often
be conveniently quantified in terms of total variation distance, for
functionals which observe part, but not all, of the combinatorial and
independent processes.
  Among the examples are combinatorial assemblies (e.g. permutations, random
mapping functions, and partitions of a set), multisets (e.g. polynomials over a
finite field, mapping patterns and partitions of an integer), and selections
(e.g. partitions of an integer into distinct parts, and square-free polynomials
over finite fields).
  We consider issues common to all the above examples, including equalities and
upper bounds for total variation distances, existence of limiting processes,
heuristics for good approximations, the relation to standard generating
functions, moment formulas and recursions for computing densities, refinement
to the process which counts the number of parts of each possible type, the
effect of further conditioning on events of moderate probability, large
deviation theory and nonuniform measures on combinatorial objects, and the
possibility of getting useful results by overpowering the conditioning.
