Structure of Population Inside Propagating Front

We study the long-time and long-range behavior of branching diffusion processes (starting with a single particle) in two different situations: when the branching potential has compact support and when the branching potential is constant. For compactly supported branching potentials we analyze the su...

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Veröffentlicht in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2013-03, Vol.189 (4), p.637-658
Hauptverfasser: Koralov, L., Molchanov, S.
Format: Artikel
Sprache:eng
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Zusammenfassung:We study the long-time and long-range behavior of branching diffusion processes (starting with a single particle) in two different situations: when the branching potential has compact support and when the branching potential is constant. For compactly supported branching potentials we analyze the super-critical case where the total number of particles grows exponentially with positive probability. We study the asymptotics of the number of particles in different regions of space and describe the growth of the region occupied by the particles. For positive constant branching potentials we observe the intermittency effect: for the number of particles located at time t in a unit neighborhood of t v the k th moment grows exponentially faster than the k th power of the first moment as t →∞ provided that v ≠ 0 and k = k (v) is sufficiently large. Bibliography: 16 titles.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-013-1212-1