Low-dimensional Distributions Research Articles

Decomposition of Multidimensional Distributions Represented by Perfect Sequences

In contrast to most other ways used to represent multidimensional probability distributions, which are based on graphical Markov modelling (i.e., dependence structure of distributions is represented by graphs), the described approach is rather procedural. Here, we describe a process by which a multidimensional distribution can be composed from a “generating sequence” – a sequence of low-dimensional distributions. This paper gives a brief introduction to this compositional approach and reports two new theorems that are necessary for designing computational procedures within this apparatus. The first concerns computation of marginal distributions, the other gives instructions for decomposing a multidimensional model into two lower-dimensional ones.

Temperature dependent relaxation rates for complex compounds in an inert medium

An earlier model for calculating zero temperature radiative and non-radiative decay rates has been extended to include relaxation from higher vibrational levels of an excited electronic state which, including the Boltzmann distribution, leads to a model that allows investigation of temperature dependence. In this procedure the lineshapes are expressed by generalized intra-molecular distributions, which can be defined by various representations. For the case where there is more than one accepting mode, intramolecular distributions of higher order have been introduced, which for certain parameter symmetries (resulting, for example, from vibrational degeneracy) can be reduced to low dimensional intramolecular distributions. Some specific intramolecular distributions are calculated using parameters which represent different vibronic coupling cases. This leads to a discussion of several types of decay rates.