A law of the iterated logarithm for iterated random walks, with application to random recursive trees

A Limit Theorem for a Nested Infinite Occupancy Scheme in Random Environment

“…In general, the definition of a branching random walk does not require that v∈I 1 P (v) = 1 a.s. A branching random walk with (− log P (v)) v∈I 1 being a globally perturbed random walk (see Section 6 for the definition) or a standard random walk is called an iterated perturbed random walk or an iterated standard random walk. Closely related to the present setting are the articles Bohun, Iksanov, Marynych, and Rashytov (2022), Iksanov, Rashytov, and Samoilenko (2023), Iksanov, Marynych, and Rashytov (2022c) and Iksanov, Kabluchko, and Kotelnikova (2022b), in which various aspects of iterated perturbed random walks and iterated standard random walks are investigated.…”