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- W2024058047 abstract "We study the possibility for branching random walks in random environment (BRWRE) to survive. The particles perform simple symmetric random walks on the $d$-dimensional integer lattice, while at each time unit, they split into independent copies according to time-space i.i.d. offspring distributions. As noted by Comets and Yoshida, the BRWRE is naturally associated with the directed polymers in random environment (DPRE), for which the quantity $Psi$ called the free energy is well studied. Comets and Yoshida proved that there is no survival when $Psi<0$ and that survival is possible when $Psi>0$. We proved here that, except for degenerate cases, the BRWRE always die when $Psi=0$. This solves a conjecture of Comets and Yoshida." @default.
- W2024058047 created "2016-06-24" @default.
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- W2024058047 date "2013-01-01" @default.
- W2024058047 modified "2023-10-08" @default.
- W2024058047 title "The critical branching random walk in a random environment dies out" @default.
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- W2024058047 doi "https://doi.org/10.1214/ecp.v18-2438" @default.
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