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

Part of: Special processes Markov processes

Published online by Cambridge University Press:  20 March 2018

Viktor Bezborodov ,
Luca Di Persio ,
Tyll Krueger ,
Mykola Lebid  and
Tomasz Ożański
Viktor Bezborodov*
Affiliation:
University of Verona
Luca Di Persio*
Affiliation:
University of Verona
Tyll Krueger*
Affiliation:
University of Wrocław
Mykola Lebid*
Affiliation:
ETH Zürich
Tomasz Ożański*
Affiliation:
University of Wrocław
*
* Postal address: Department of Computer Science, The University of Verona, Strada le Grazie 15, Verona, 37134, Italy.
* Postal address: Department of Computer Science, The University of Verona, Strada le Grazie 15, Verona, 37134, Italy.
*** 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.
*** Postal address: Department of Computer Science and Engineering, Wrocław University of Technology, Janiszewskiego 15, Wrocław, 50-372, Poland.
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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.

Keywords

Shape theoremspatial birth processgrowth model

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
Original Article
Information
Advances in Applied Probability , Volume 50 , Issue 1 , March 2018 , pp. 74 - 101
Copyright
Copyright © Applied Probability Trust 2018 

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