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In equilibrium statistical mechanics, the density of microstates representing the statistical weight associated with a partition of an isolated system into subsystems (fragments) is the convolution of the state densities of the component subsystems. The Laplace transform approximation provides a simple representation of this density. Despite the fact that no external heat bath can be said to exist (the canonical ensemble is not appropriate) the approximation leads to partition probabilities that involve a product of factors (one for each fragment) expressed in terms of a characteristic inverse temperature. We apply the method to nuclear multifragmentation with particular emphasis on a transition that occurs when the major part of the available energy appears as kinetic (as opposed to internal excitation) energy of fragments. Finally, we discuss the shortcomings and advantages of expressing the weights of partitions with fixed total mass (charge) and multiplicity in a simple multinomial form.

When a matrix is reduced to Lanczos tridiagonal form, its matrix elements can be divided into an analytic smooth mean value and a fluctuating part. The next-neighbor spacing distribution P(s) and the spectral rigidity $\Delta_3$ are shown to be universal functions of the average value of the fluctuating part. It is explained why the behavior of these quantities suggested by random matrix theory is valid in far more general cases.

In fragmentation of a finite object such as an atomic nucleus or a percolation lattice, the multidimensional probability distribution of the numbers of fragments of each mass (charge, size) may be approximated as a product of Poisson distributions. In this work we present an analytical treatment of the influence of constraints (multiplicity, mass, etc.) that may be imposed on the basic product distribution.