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Asymptotic shape and the speed of propagation of continuous-time continuous-space birth processes

  • Viktor Bezborodov (a1), Luca Di Persio (a1), Tyll Krueger (a2), Mykola Lebid (a3) and Tomasz Ożański (a2)...

Abstract

We formulate and prove a shape theorem for a continuous-time continuous-space stochastic growth model under certain general conditions. Similar to the classical lattice growth models, the proof makes use of the subadditive ergodic theorem. A precise expression for the speed of propagation is given in the case of a truncated free-branching birth rate.

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Corresponding author

* Postal address: Department of Computer Science, The University of Verona, Strada le Grazie 15, Verona, 37134, Italy.
** Email address: viktor.bezborodov@univr.it
*** Postal address: Department of Computer Science and Engineering, Wrocław University of Technology, Janiszewskiego 15, Wrocław, 50-372, Poland.
**** Postal address: Department of Biosystems Science and Engineering, ETH Zürich, D-BSSE, Mattenstrasse 26, Basel, 4058, Switzerland.

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