Large deviations analysis for random combinatorial partitions with counter terms

Large deviations for integer partitions

We consider deviations from limit shape induced by uniformly distributed partitions (and strict partitions) of an integer n on the associated Young diagrams. We prove a full large deviation principle, of speed p n. The proof, based on projective limits, uses the representation of the uniform measure on partitions by means of suitably conditioned independent variables.

Large Deviations for Random Trees.

We consider large random trees under Gibbs distributions and prove a Large Deviation Principle (LDP) for the distribution of degrees of vertices of the tree. The LDP rate function is given explicitly. An immediate consequence is a Law of Large Numbers for the distribution of vertex degrees in a large random tree. Our motivation for this study comes from the analysis of RNA secondary structures.

Large Deviations for Random Walk in Random

Large Deviations of Divergence Measures on Partitions

We discuss Chernoo-type large deviation results for the total variation , the I-divergence errors, and the 2-divergence errors on partitions. In contrast to the total variation and the I-divergence, the 2-divergence has an unconventional large deviation rate. Applications to Bahadur eeciencies of goodness-of-t tests based on these divergence measures for multivariate observations are given.

Large Deviations for Slotted ALOHA Random Access

The effective bandwidth of a source measures the amount of burstiness besides the data generation rate. The effective bandwidths provide a means to guarantee qualityof-service in terms of packet loss probabilities. The classical theory of effective bandwidth, however, does not apply to a random access system, since the queues are coupled, i.e., the service statistics at one queue depend on the ...