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Zapiski Nauchnykh Seminarov POMI, 2009, Volume 364, Pages 109–119 (Mi znsl3153)  

Ergodic properties of crystallization processes

Yu. Davydova, A. Illigb

a Universite of Lille 1, France
b University of Versailles Saint-Quentin, France
References:
Abstract: We consider a birth and growth processes with germs being born according to a Poisson point processes whose intensity measure is invariant under translations in space. The germs can be born in unoccupied space and then start growing until they occupy the available space. In this general framework, the crystallization process can be characterized by a random field which, for any point in the state space, assigns the first time at which this point is reached by a crystal. Under general conditions on the growth speed and goemetrical shape of free crystals, we prove that the random field is mixing in the sense of ergodic theory. This result is illustrated by applications to the problem of parameter estimation. Bibl. – 7 titles.
Received: 16.12.2007
English version:
Journal of Mathematical Sciences (New York), 2010, Volume 163, Issue 4, Pages 375–381
DOI: https://doi.org/10.1007/s10958-009-9680-z
Bibliographic databases:
UDC: 519
Language: English
Citation: Yu. Davydov, A. Illig, “Ergodic properties of crystallization processes”, Probability and statistics. Part 14–2, Zap. Nauchn. Sem. POMI, 364, POMI, St. Petersburg, 2009, 109–119; J. Math. Sci. (N. Y.), 163:4 (2010), 375–381
Citation in format AMSBIB
\Bibitem{DavIll09}
\by Yu.~Davydov, A.~Illig
\paper Ergodic properties of crystallization processes
\inbook Probability and statistics. Part~14--2
\serial Zap. Nauchn. Sem. POMI
\yr 2009
\vol 364
\pages 109--119
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl3153}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2010
\vol 163
\issue 4
\pages 375--381
\crossref{https://doi.org/10.1007/s10958-009-9680-z}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-70549103374}
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