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Distributions of cherries and pitchforks for the Ford model
Gursharn Kaur, Kwok Pui Choi, Taoyang Wu
We study two fringe subtree counting statistics, the number of cherries and that of pitchforks for Ford's model, a one-parameter family of random phylogenetic tree models that…
On asymptotic joint distributions of cherries and pitchforks for random phylogenetic trees
Kwok Pui Choi, Gursharn Kaur, Taoyang Wu
Tree shape statistics provide valuable quantitative insights into evolutionary mechanisms underpinning phylogenetic trees, a commonly used graph representation of evolution systems…
Negatively Reinforced Balanced Urn Schemes
Gursharn Kaur
We consider weighted negatively reinforced urn schemes with finitely many colours. An urn scheme is called negatively reinforced, if the selection probability for a colour is propo…
Generalized Pólya Urn Schemes with Negative but Linear Reinforcements
Antar Bandyopadhyay, Gursharn Kaur
In this paper, we consider a new type of urn scheme, where the selection probabilities are proportional to a weight function, which is linear but decreasing in the proportion of ex…