Abstract
Consider sequential packing of unit volume balls in a large cube, in any dimension and with Poisson input. We show after suitable rescaling that the spatial distribution of packed balls tends to that of a Gaussian field in the thermodynamic limit. The results cover related applied models, including ballistic deposition and spatial birth-growth models.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
Z. Adamczyk, B. Siwek, M. Zembala, and P. Belouschek, Kinetics of localized adsorption of colloid particles, Adv. in Colloid and Interface Sci. 48:151-280 (1994).
A.-L. Barabási and H. E. Stanley, Fractal Concepts in Surface Growth (Cambridge University Press, 1995).
M. C. Bartelt and V. Privman, Kinetics of irreversible monolayer and multilayer sequential adsorption, Internat. J. Mod. Phys. B 5:2883-2907 (1991).
Yu. Baryshnikov, Supporting-points processes and some of their applications, Probab. Theory Related Fields 117:163-182 (2000).
P. Billingsley, Convergence of Probability Measures (Wiley, 1968).
S. N. Chiu and M. P. Quine, Central limit theory for the number of seeds in a growth model in ℝd with inhomogeneous Poisson arrivals, Ann. Appl. Probab. 7:802-814 (1997).
E. G. Coffman, L. Flatto, P. Jelenkoviác, and B. Poonen, Packing random intervals on-line, Algorithmica 22:448-476 (1998).
A. Dvoretzky and H. Robbins, On the "parking" problem, MTA Mat Kut. Int. Küzl., (Publications of the Math. Res. Inst. of the Hungarian Academy of Sciences) 9:209-225 (1964).
J. W. Evans, Random and cooperative adsorption, Rev. Modern Phys. 65:1281-1329 (1993).
J. M. Garcia-Ruiz, E. Louis, P. Meakin, and L. Sander, Growth Patterns in Physical Sciences and Biology (Plenum Press, New York, 1993).
D. Iagolnitzer and B. Souillard, Random fields and limit theorems, Colloquia Mathematica Soc. János Bolyai (Random Fields) 27:573-591 (1979).
Y. Itoh and L. Shepp, Parking cars with spin but no length, J. Stat. Phys. 97:209-231 (1999).
G. Ivanoff, Central limit theorems for point processes, Stoch. Proc. Appl. 12:171-186 (1982).
V. A. Malyshev, The central limit theorem for Gibbsian random fields, Sov. Math. Dokl. 16:1141-1145 (1975).
I. Molchanov, Statistics of the Boolean Model for Practitioners and Mathematicians (Wiley, 1997).
M. D. Penrose, Random parking, sequential adsorption, and the jamming limit, Comm. Math. Phys. 218:153-176 (2001).
M. D. Penrose, Limit theory for monolayer ballistic deposition in the continuum, J. Stat. Phys. 105:561-583 (2001).
M. D. Penrose, Limit theorems for monotonic particle systems and sequential deposition, Stochastic Proc. and Their Applic. 98:175-197 (2002).
M. D. Penrose and J. E. Yukich, Central limit theorems for some graphs in computational geometry, Ann. Appl. Probab. 11:1005-1041 (2001).
M. D. Penrose and J. E. Yukich, Limit theory for random sequential packing and deposition, Ann. Appl. Probab. 12:272-301 (2001).
V. Privman, Adhesion of submicron particles on solid surfaces. A special issue of Colloids and Surfaces A 165, V. Privman, ed. (2000).
D. Ruelle, Statistical Mechanics: Rigorous Results (Benjamin, Amsterdam, 1970).
B. Senger, J.-C. Voegel, and P. Schaaf, Irreversible adsorption of colloidal particles on solid substrates, Colloids and Surfaces A 165:255-285 (2000).
H. Solomon, Random packing density, Proc. Fifth Berkeley Symp. on Prob. and Stat., Vol. 3 (University California Press, 1967), pp. 119-134.
D. Stoyan and H. Stoyan, Fractals, Random Shapes and Point Fields (Wiley, 1994).
J. Talbot, G. Tarjus, P. R. Van Tassel, and P. Viot, From car parking to protein adsorption: An overview of sequential adsorption processes, Colloids and Surfaces A 165:287-324 (2000).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Baryshnikov, Y., Yukich, J.E. Gaussian Fields and Random Packing. Journal of Statistical Physics 111, 443–463 (2003). https://doi.org/10.1023/A:1022229713275
Issue Date:
DOI: https://doi.org/10.1023/A:1022229713275