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math.PR2020
Preferential attachment with fitness dependent choice
Yury Malyshkin
We study the asymptotic behavior of the maximum degree in the evolving tree model with a choice based on both degree and fitness of a vertex. The tree is constructed in the followi…
math.PR2020
MSO 0-1 law for recursive random trees
Y. A. Malyshkin, M. E. Zhukovskii
We prove the monadic second order 0-1 law for two recursive tree models: uniform attachment tree and preferential attachment tree. We also show that the first order 0-1 law does no…
math.PR2019
Sublinear preferential attachment combined with the growing number of choices
Yury Malyshkin
We prove almost sure convergence of the maximum degree in an evolving graph model combining a growing number of local choices with sublinear preferential attachment. At each step i…