Geodesic
Ergodic properties of crystallization processes
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 14–2, Tome 364 (2009), pp. 109-119 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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Yu. Davydov; A. Illig. Ergodic properties of crystallization processes. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 14–2, Tome 364 (2009), pp. 109-119. http://geodesic.mathdoc.fr/item/ZNSL_2009_364_a4/

[1] A. N. Kolmogorov, “Statistical theory of crystallization of metals”, Bull. Acad. Sci. USSR Mat. Ser., 1 (1937), 355–359

[2] J. Møller, “Random tessellations in $\mathbf R^d$”, Adv. Appl. Probab., 21 (1989), 37–73 | DOI | MR

[3] J. Møller, “Random Johnson–Mehl tessalations”, Adv. Appl. Probab., 24 (1992), 814–844 | DOI | MR

[4] J. Møller, “Generation of Johnson–Mehl crystals and comparative analysis of models for random nucleation”, Adv. Appl. Probab., 27 (1995), 367–383 | DOI | MR

[5] Yu. Davydov, A. Illig, Ergodic properties of geometrical crystallization processes. I, E-print , 2006 arxiv: org.math/0610966 | MR

[6] W. A. Johnson, R. F. Mehl, “Reaction kinetics in processes and growth”, Trans. Amer. Inst. Min. Metal. Petro. Eng., 135 (1939), 416–458

[7] A. Micheletti, V. Capasso, “Stochastic geometry of polymer crystallization processes”, Stochastic Anal. Appl., 15:3 (1997), 355–373 | DOI | MR | Zbl