Summary
Let\(\mathfrak{X}\) denote a branching random walk in\(\mathbb{R}^1 \) with mean particle productionm, m>1, and with incremental spatial distributionG, withG({0}) =p andG({1})=1−p. Ifmp=1, then the minimal displacement of\(\mathfrak{X}\) behaves asymptotically like log logn/log 2. If the conditionG({1})=1−p is replaced byG((0, ∞))=1−p, we obtain a similar result.
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Research was partially supported by the National Science Foundation under grant MCS-7607039
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Bramson, M.D. Minimal displacement of branching random walk. Z. Wahrscheinlichkeitstheorie verw Gebiete 45, 89–108 (1978). https://doi.org/10.1007/BF00715186
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DOI: https://doi.org/10.1007/BF00715186