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.

Introduction. Some fruit characteristics are very important for cherry marketing. This study aimed at determining relationships between some of them to help researchers on fruit quality. Materials and methods. The relationships between fruit cracking, fruit weight and diameter, soluble solid and acidity content, and fruit stalk thickness were determined on 35 sweet cherry cultivars in Amasya in Turkey. Results and discussion. There was a positive polynomial relationship between the fruit stalk thickness and fruit cracking; between fruit weight and fruit stalk thickness; and between fruit weight and fruit firmness. There was a positive relationship between the fruit weight and the acidity content, and between the fruit firmness, acidity and soluble solid. There was a negative relationship between fruit firmness and pH. Conclusions. Some relationships between cherry characteristics exist, which may help researchers to solve some problems such as fruit cracking. These studies may contribute to producing fruit with a good quality and help to evaluate new cultivars.