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- W3100322488 abstract "Construct recursively a long string of words $$w_1,ldots w_n,$$ such that at each step k, $$w_{k+1}$$ is a new word with a fixed probability $$pin (0,1),$$ and repeats some preceding word with complementary probability $$1-p.$$ More precisely, given a repetition occurs, $$w_{k+1}$$ repeats the jth word with probability proportional to $$j^{alpha }$$ for $$j=1,ldots , k.$$ We show that the proportion of distinct words occurring exactly $$ell $$ times converges as the length n of the string goes to infinity to some probability mass function in the variable $$ell ge 1,$$ whose tail decays as a power function when $$p<1/(1+alpha ),$$ and exponentially fast when $$p>1/(1+alpha ).$$" @default.
- W3100322488 created "2020-11-23" @default.
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- W3100322488 date "2019-05-22" @default.
- W3100322488 modified "2023-09-27" @default.
- W3100322488 title "A Version of Herbert A. Simon’s Model with Slowly Fading Memory and Its Connections to Branching Processes" @default.
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- W3100322488 doi "https://doi.org/10.1007/s10955-019-02316-1" @default.
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