24 citations · 195 across the 74 of their papers we have counts for
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A result on power moments of Lévy-type perpetuities and its application to the -convergence of Biggins' martingales in branching Lévy processes
Alexander Iksanov, Bastien Mallein
Lévy-type perpetuities being the a.s. limits of particular generalized Ornstein-Uhlenbeck processes are a natural continuous-time generalization of discrete-time perpetuities. Thes…
On nested infinite occupancy scheme in random environment
Alexander Gnedin, Alexander Iksanov
We consider an infinite balls-in-boxes occupancy scheme with boxes organised in nested hierarchy, and random probabilities of boxes defined in terms of iterated fragmentation of a…
Weak convergence of the number of vertices at intermediate levels of random recursive trees
Alexander Iksanov, Zakhar Kabluchko
Let be the number of vertices at level in a random recursive tree with vertices. We are interested in the asymptotic behavior of for intermediate levels…
Fluctuations of Biggins' martingales at complex parameters
Alexander Iksanov, Konrad Kolesko, Matthias Meiners
The long-term behavior of a supercritical branching random walk can be described and analyzed with the help of Biggins' martingales, parametrized by real or complex numbers. The st…
Stable limit laws for random walk in a sparse random environment I: moderate sparsity
Dariusz Buraczewski, Piotr Dyszewski, Alexander Iksanov +2
A random walk in a sparse random environment is a model introduced by Matzavinos et al. [Electron. J. Probab. 21, paper no. 72: 2016] as a generalization of both a simple symmetric…
A functional limit theorem for the profile of random recursive trees
Alexander Iksanov, Zakhar Kabluchko
Let be the number of vertices at level in a random recursive tree with vertices. We prove a functional limit theorem for the vector-valued process $(X_{[n^t]}(1)…