Growth and Structure of Stochastic Sequences
E. Ben-Naim and P.L. Krapivsky
We introduce a class of stochastic integer sequences. In these
sequences, every element is a sum of two previous elements, at least
one of which is chosen randomly. The interplay between randomness
and memory underlying these sequences leads to a wide variety of
behaviors ranging from stretched exponential to log-normal to
algebraic growth. Interestingly, the set of all possible sequence
values has an intricate structure.
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