The strong Malthusian behavior of growth-fragmentation processes
| Autor: | Alexander R. Watson, Jean Bertoin |
|---|---|
| Přispěvatelé: | University of Zurich, Institut für Mathematik [Zürich], Universität Zürich [Zürich] = University of Zurich (UZH), School of Mathematics [Manchester], University of Manchester [Manchester] |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Work (thermodynamics)
Spectral theory 340 Law Ocean Engineering 610 Medicine & health Growth-fragmentation process 01 natural sciences 010104 statistics & probability 510 Mathematics Fragment (logic) Exponential ergodicity Convergence (routing) FOS: Mathematics Statistical physics 0101 mathematics Mathematics Malthus behavior 010102 general mathematics Probability (math.PR) Fragmentation (computing) Exponential function branching process [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] 10123 Institute of Mathematics Mathematics - Probability intrinsic martingale |
| Popis: | Growth-fragmentation processes describe the evolution of systems of cells which grow continuously and fragment suddenly; they are used in models of cell division and protein polymerisation. Typically, we may expect that in the long run, the concentrations of cells with given masses increase at some exponential rate, and that, after compensating for this, they arrive at an asymptotic profile. Up to now, this question has mainly been studied for the average behavior of the system, often by means of a natural partial integro-differential equation and the associated spectral theory. However, the behavior of the system as a whole, rather than only its average, is more delicate. In this work, we show that a criterion found by one of the authors for exponential ergodicity on average is actually sufficient to deduce stronger results about the convergence of the entire collection of cells to a certain asymptotic profile, and we find some improved explicit conditions for this to occur. |
| Databáze: | OpenAIRE |
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