On a special class of gibbs hard-core point processes modeling random patterns of non-overlapping grains

References

• Dereudre, D. ( 2019). Introduction to the theory of Gibbs point processes. In Stochastic Geometry 181–229. Lecture Notes in Math., 2237, Springer, Cham.
   Google Scholar
• Chiu, S. N., Stoyan, D., Kendall, W. S., Mecke, J. ( 2013). Stochastic Geometry and its Applications, 3th ed. Chichester, UK: Wiley.
   Google Scholar
• Van Lieshout, M. N. M. ( 2000). Markov Point Processes and their Applications. London, UK: Imperial College Press.
   Google Scholar
• Strauss, D. J. ( 1975). A model for clustering. Biometrika. 62(2): 467–475. doi:10.1093/biomet/62.2.467.
   Web of Science ®Google Scholar
• Sudbrack, C. K., Ziebell, T. D., Noebe, R. D., Seidman, D. N. ( 2008). Effects of a tungsten addition on the morphological evolution, spatial correlations and temporal evolution of a model Ni–Al–Cr superalloy. Acta Mater. 56(3): 448–4463. doi:10.1016/j.actamat.2007.09.042.
   Web of Science ®Google Scholar
• Quested, T. E., Greer, A. L. ( 2005). Grain refinement of Al alloys: Mechanisms determining as-cast grain size in directional solidification. Acta Mater. 53(17): 4643–4653. doi:10.1016/j.actamat.2005.06.018.
   Web of Science ®Google Scholar
• Shu, D., Sun, B., Mi, J., Grant, P. S. ( 2011). A quantitative study of solute diffusion field effects on heterogeneous nucleation and the grain size of alloys. Acta Mater. 59(5): 2135–2144. doi:10.1016/j.actamat.2010.12.014.
   Web of Science ®Google Scholar
• Prasad, A., Yuan, L., Lee, P. D., StJohn, D. H. ( 2013). The Interdependence model of grain nucleation: A numerical analysis of the nucleation-free zone. Acta Mater. 61(16): 5914–5927. doi:10.1016/j.actamat.2013.06.015.
   Web of Science ®Google Scholar
• Ventura, H. S., Alves, A. L., Assis, W. L., Villa, E., Rios, P. R. ( 2018). Influence of an exclusion radius around each nucleus on the microstructure and transformation kinetics. Materialia. 2:167–175. doi:10.1016/j.mtla.2018.07.009.
   Google Scholar
• Andersson, J., Häggström, O., Maansson, M. ( 2006). The volume fraction of a non-overlapping germ-grain model. Electron. Commun. Probab. 11:78–88.
   Web of Science ®Google Scholar
• Hirsch, C., Last, G. ( 2018). On maximal hard-core thinnings of stationary particle Processes. J. Stat. Phys. 170(3):554–583. doi:10.1007/s10955-017-1943-3.
   Web of Science ®Google Scholar
• Kiderlen, M., Hörig, M. ( 2013). Matérn’s hard core models of types I and II with arbitrary compact grains. CSGB Research Report No. 5. Aarhus, Denmark: Centre for Stochastic Geometry and Advanced Bioimaging, Aarhus University.
   Google Scholar
• Mønsson, M., Rudemo, M. ( 2002). Random patterns of nonoverlapping convex grains. Adv. Appl. Probab. 34(4): 718–738. doi:10.1239/aap/1037990950.
   Web of Science ®Google Scholar
• Teichmann, J., Ballani, F., Van Den Boogaart, K. G. ( 2013). Generalizations of Matérn’s hard-core point processes. Spat. Stat. 3: 33–53. doi:10.1016/j.spasta.2013.02.001.
   Web of Science ®Google Scholar
• Daniel, J., Horrocks, J., Umphrey, G. J. ( 2018). Penalized composite likelihoods for inhomogeneous Gibbs point process models. Comput. Stat. Data Anal. 124:104–116. doi:10.1016/j.csda.2018.02.005.
   Web of Science ®Google Scholar
• Mase, S. ( 1986). On the possible form of size distributions for Gibbsian processes of mutually non-intersecting balls. J. Appl. Probab. 23(3):646–659. doi:10.2307/3214003.
   Web of Science ®Google Scholar
• Jensen, E. B. V., Nielsen, L. S. ( 2001). A review on inhomogeneous Markov point processes. Lect. Notes-Monogr. Ser. 37:297–318.
   Google Scholar
• Bondesson, L., Fahlen, J. ( 2003). Mean and variance of vacancy for hard-core disc processes and applications. Scand. J. Stat. 30(4): 797–816. doi:10.1111/1467-9469.00365.
   Web of Science ®Google Scholar
• Coeurjolly, J. F., Lavancier, F. ( 2018). Intensity approximation for pairwise interaction Gibbs point processes using determinantal point processes. Electron. J. Stat. 12(2): 3181–3203.
   Web of Science ®Google Scholar
• Baddeley, A., Nair, G. ( 2012). Fast approximation of the intensity of Gibbs point processes. Electron. J. Stat. 6:1155–1169.
   Web of Science ®Google Scholar
• Ba, I., Coeurjolly, J. F. ( 2020). Inference for low and high dimensional inhomogeneous Gibbs point processes, To appear in Scand. J. Stat.
   Google Scholar
• Daley, D. J., Vere-Jones, D. ( 2003). An Introduction to the Theory of Point Processes. Vol. I. Elementary theory and Methods, New York, NY: Springer.
   Google Scholar
• Daley, D. J., Vere-Jones, D. ( 2008). An introduction to the theory of point processes. In General Theory and Structure. New York, NY: Springer.
   Google Scholar
• Last, G., Brandt, A. ( 1995). Marked Point Processes on the Real Line. The Dynamic Approach. New York, NY: Springer.
   Google Scholar
• Matheron, G. ( 1975). Random Sets and Integral Geometry. New York, NY: Wiley.
   Google Scholar
• Molchanov, I. ( 1997). Statistics of the Boolean Model for Practitioners and Mathematicians. New York, NY: Wiley.
   Google Scholar
• Molchanov, I. ( 2005). Theory of Random Sets. London, UK: Springer-Verlag.
   Google Scholar
• Schneider, R., Weil, W. ( 2008). Stochastic and Integral Geometry. Berlin, Germany: Springer-Verlag.
   Google Scholar
• Kingman, J. F. C. ( 1993). Poisson Processes. Oxford, UK: Oxford University Press.
   Google Scholar
• Last, G., Penrose, M. ( 2018). Lectures on the Poisson Process. Cambridge, UK: Cambridge University Press.
   Google Scholar
• Baddeley, A., Bárány, I., Schneider, R., Weil, W. ( 2007). Stochastic geometry. In W. Weil eds. Lecture Notes in Math: Berlin: Springer, p. 1892.
   Google Scholar
• Papangelou, F. ( 1974). The conditional intensity of general point processes and an application to line processes. Z Wahrscheinlichkeitstheorie Verw. Gebiete. 28(3): 207–226. doi:10.1007/BF00533242.
   Google Scholar
• Kallenberg, O. ( 1984). An informal guide to the theory of conditioning in point processes. Int. Stat. Rev. / Revue Internationale De Statistique. 52(2): 151. doi:10.2307/1403098.
   Web of Science ®Google Scholar
• Georgii, H.-O. ( 1976). Canonical and grand canonical Gibbs states for continuum systems. Commun. Math. Phys. 48(1): 31–51. doi:10.1007/BF01609410.
   Web of Science ®Google Scholar
• Nguyen, X. X., Zessin, H. ( 1977). Integral and differential characterizations of the Gibbs process. Adv. Appl. Probab. 9(3): 446–447. doi:10.2307/1426106.
   Web of Science ®Google Scholar
• Van Lieshout, M. N. M. ( 1997). On likelihoods for Markov random sets and Boolean models. In: Jeulin, D., ed., Proceedings of the International Symposium on Advances in Theory and Applications of Random Sets. Singapore: World Scientific, pp. 121–136.
   Google Scholar
• Villa, E. ( 2014). On the local approximation of mean densities of random closed sets. Bernoulli. 20(1): 1–27.
   Web of Science ®Google Scholar
• Hug, D., Last, G. ( 2000). On support measures in Minkowski spaces and contact distributions in stochastic geometry. Ann. Probab. 28(2):796–850.
   Web of Science ®Google Scholar
• Dereudre, D., Vasseur, T. ( 2020). Existence of Gibbs point processes with stable infinite range interaction. J. Appl. Probab. 57(3): 775–791. doi:10.1017/jpr.2020.39.
   Web of Science ®Google Scholar
• Møller, J., Waagepetersen, R. P. ( 2004). Statistical Inference and Simulation for Spatial Point Processes. Boca Raton, FL: Chapman and Hall/CRC.
   Google Scholar
• Stucki, K., Schuhmacher, D. ( 2014). Bounds for the probability generating functional of a Gibbs point process. Adv. Appl. Probab. 46(1): 21–34. doi:10.1239/aap/1396360101.
   Web of Science ®Google Scholar
• Hansen, N. ( 1990). Cold deformation microstructures. Mater. Sci. Technol. 6(11): 1039–1047. doi:10.1179/mst.1990.6.11.1039.
   Web of Science ®Google Scholar
• Tanaka, T. ( 1981). Controlled rolling of steel plate and strip. Int. Metals Rev. 26(1): 185–212. doi:10.1179/imtr.1981.26.1.185.
   Google Scholar
• Oyama, T., Watanabe, C., Monzen, R. ( 2016). Growth kinetics of ellipsoidal ω-precipitates in a Ti–20%wt Mo alloy under compressive stress. J. Mater. Sci. 51(19): 8880–8887. doi:10.1007/s10853-016-0135-x.
   Web of Science ®Google Scholar
• Shepilov, M. P., Baik, D. S. ( 1994). Computer simulation of crystallization kinetics for the model with simultaneous nucleation of randomly-oriented ellipsoidal crystals. J. Non-Cryst. Solids. 171(2): 141–156. doi:10.1016/0022-3093(94)90350-6.
   Web of Science ®Google Scholar
• Weinberg, M. C., Birnie, D. P. ( 1995). Transformation kinetics for randomly oriented anisotropic particles. J. Non-Cryst. Solids. 189(1-2): 161–166. doi:10.1016/0022-3093(95)00226-X.
   Web of Science ®Google Scholar
• Villa, E., Rios, P. R. ( 2020). On volume and surface densities of dynamical germ-grain models with ellipsoidal growth: A rigorous approach with applications to materials science. Stoch. Anal. Appl. 38(6): 1134–1155. doi:10.1080/07362994.2020.1773276.
   Web of Science ®Google Scholar
• Yan, Y., Chirikjian, G. S. ( 2015). Closed-form characterization of the Minkowski sum and difference of two ellipsoids. Geom. Dedicata. 177(1): 103–128. doi:10.1007/s10711-014-9981-3.
   Web of Science ®Google Scholar
• Jalilian, A., Guan, Y., Waagepetersen, R. ( 2019). Orthogonal series estimation of the pair correlation function of a spatial point process. Statist. Sinica. 29(2): 769–787.
   Web of Science ®Google Scholar
• Cahn, J. W., Cahn, J. ( 1995). Time cone method for nucleation and growth kinetics on a finite domain. MRS Proc. 398: 425–437.
   Google Scholar
• Coeurjolly, J., Møller, J., Waagepetersen, R. ( 2017). A tutorial on palm distributions for spatial point processes. Int. Stat. Rev. 85(3): 404–420. doi:10.1111/insr.12205.
   Web of Science ®Google Scholar
• Haengii, M. ( 2012). Stochastic Geometry for Wireless Networks. Cambridge, UK: Cambridge University Press.
   Google Scholar