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Supercritical Spatially Homogeneous Branching in Admits no Equilibria
Author(s) -
Matthes Klaus,
Nawrotzki Kurt,
Siegmund – Schultze Rainer
Publication year - 2001
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/1522-2616(200107)227:1<109::aid-mana109>3.0.co;2-x
Subject(s) - mathematics , branching (polymer chemistry) , homogeneous , euclidean geometry , supercritical fluid , criticality , statistical physics , euclidean space , pure mathematics , branching process , combinatorics , geometry , physics , thermodynamics , materials science , nuclear physics , composite material
At the beginning of investigations in spatially homogeneous branching processes in Euclidean space ( Liemant [1]) it seemed to be obvious that the existence of equilibria implies criticality of branching. This prejudice was disproved by the example [2] of a subcritical homogeneous branching equilibrium in dimension one. We prove that supercritical homogeneous branching processes in Euclidean space and, more general, in a broad class of topological groups have no (non – void, homogeneous) equilibria.