Derives decoupling conditions for fluctuating-growth size-structured populations and connects them to Feynman-Kac formula via random time changes and exponential tilting.
Steady distribution of the incremental model for bacteria proliferation
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abstract
We study the mathematical properties of a model of cell division structured by two variables, the size and the size increment, in the case of a linear growth rate and a self-similar fragmentation kernel. We first show that one can construct a solution to the related two dimensional eigenproblem associated to the eigenvalue 1 from a solution of a certain one dimensional fixed point problem. Then we prove the existence and uniqueness of this fixed point in the appropriate $\mathrm{L}^1$ weighted space under general hypotheses on the division rate. Knowing such an eigenfunction proves useful as a first step in studying the long time asymptotic behaviour of the Cauchy problem.
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UNVERDICTED 2representative citing papers
In this oriented branching-and-fusion network, the empirical measure of rectangle sizes converges after polynomial rescaling to an explicit limiting distribution whose speed of convergence is also derived.
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Size-structured populations with growth fluctuations: Feynman--Kac formula and decoupling
Derives decoupling conditions for fluctuating-growth size-structured populations and connects them to Feynman-Kac formula via random time changes and exponential tilting.
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Growing random planar network with oriented branching and fusion
In this oriented branching-and-fusion network, the empirical measure of rectangle sizes converges after polynomial rescaling to an explicit limiting distribution whose speed of convergence is also derived.