Geodesic
Criticality conditions in the Derrida–Retaux model with a random number of terms
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 36, Tome 535 (2024), pp. 141-149 Cet article a éte moissonné depuis la source Math-Net.Ru

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The article considers the Derrida–Retaux model with a random number of terms, i.e. a sequence of integer random variables defined by the relations $ X_{n + 1} = (X_n^{(1)} +\cdots + X_n^{(N_n)} - a)^{+}$, $n\ge 0$, where $X_n^{(j)}$ are independent copies of $X_n$, the values of $N_j$ are independent and identically distributed, $a$ is a positive integer. The energy in the model is defined as $Q:=\lim\limits_{n\to\infty} \frac{\mathbf{E} (X_{n})}{(\mathbf{E} N_1)^{n}}$. We present sufficient conditions (in terms of distributions of $X_0$ and $N_1$) for subcritical ($Q=0$) and supercritical ($Q>0$) regimes of model behavior. 
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     title = {Criticality conditions in the {Derrida{\textendash}Retaux} model with a random number of terms},
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A. A. Kotova; A. S. Lotnikov. Criticality conditions in the Derrida–Retaux model with a random number of terms. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 36, Tome 535 (2024), pp. 141-149. http://geodesic.mathdoc.fr/item/ZNSL_2024_535_a9/

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