Large Deviations for Random Trees

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.

Random Trees, Heights, and Large Deviations

Random trees are of prime importance for studying the average case behavior of algorithms and data structures. The canonical examples are Hoare’s quicksort algorithm and the binary search tree. The most natural parameter to study is the average running time of the algorithm, and the average time for answering a query in a data structure. This does not provide sufficient information to properly ...

Large Deviations for the Leaves in Some Random Trees

Large deviation principles and related results are given for a class of Markov chains associated to the “leaves” in random recursive trees and preferential attachment random graphs, as well as the “cherries” in Yule trees. In particular, the method of proof, combining analytic and Dupuis-Ellis type path arguments, allows for an explicit computation of the large deviation pressure.

Large deviations of Markov hains indexed by random trees

Large Deviations for Random Walk in Random