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In the present paper, we provide exact expressions and sharp asymptotics for the covariance matrix of a dichromatic time-dependent Pólyaurn. We follow a purely combinatorial approach. Although we take interest in the large-index case with a fixed ...

Do the rich always get richer by investing in a cryptocurrency for which new coins are issued according to a proof-of-stake (PoS) protocol? We answer this question in the negative: Without trading, the investor shares in the cryptocurrency are martingales ...

We investigate the joint distribution of nodes of small degrees and the degree profile in preferential dynamic attachment circuits. In particular, we study the joint asymptotic distribution of the number of the nodes of outdegree 0 (terminal nodes)...

We investigate node degrees in a network grown from a seed by hooking self-similar components under two models of randomness: a uniform attachment model and a model based on preferential attachment. We study two degree profiles: a ...

Cumulative advantage (CA) refers to the notion that accumulated resources foster the accumulation of further resources in competitions, a phenomenon that has been empirically observed in various contexts. The oldest and arguably simplest mathematical ...

We study necessary and sufficient conditions for the strong tenability of Pólya urn schemes under the sampling of multisets of balls. We also investigate sufficient conditions for the tenability (not necessarily in the strong sense) of Pólya urn ...

The multinomial language model has been one of the most effective models of retrieval for more than a decade. However, the multinomial distribution does not model one important linguistic phenomenon relating to term dependency—that is, the tendency of a ...

We study a generalized Friedman's urn model with multiple drawings of white and blue balls. After a drawing, the replacement follows a policy of opposite reinforcement. We give the exact expected value and variance of the number of white balls after a ...