Limit theorems for stochastic dynamical system arising in ising model analysis

• Autorzy: Szwarc R. , Topolski K.
• Języki publikacji: EN

Abstrakty

EN

A simple stochastic dynamical system defined on the space of doubly-infinite sequences of real numbers is considered. Limit theorems for this system are proved. The results are applied to the physical model of wetting of the flat heterogeneous wall.

Słowa kluczowe

EN

Markov chain; random transformation; weak convergence; Ising model; wetting

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2008
• Tom: Vol. 28, Fasc. 2
• Strony: 257--270
• Opis fizyczny: Bibliogr.13 poz.

Twórcy

autor

Szwarc R.

• Institute of Mathematics, Wrocław University, pl. Grunwaldzki 2/4 50-384 Wrocław, Poland
• Institute of Mathematics and Computer Science, University of Opole, ul. Oleska 48, 45-052 Opole, Poland

autor

Topolski K.

• Institute of Mathematics, Wrocław University, pl. Grunwaldzki 2/4 50-384 Wrocław, Poland

Bibliografia

• [1] D. B. Abraham, Surface Structures and Phase Transitions-exact Results, Phase Transit. Crit. Phenom. Vol. 10, Academic Press, 1986.
• [2] A. W. Adamson, Physical Chemistry of Surfaces, Wiley, New York 1976.
• [3] P. Billingsley, Convergence of Probability Measures, Wiley, New York 1968.
• [4] K. Binder, Critical Behaviour at Surfaces in Phase Transitions and Critical Phenomena, Phase Transit. Crit. Phenom. Vol. 8, Academic Press, 1983.
• [5] A. B. D. Cassie, Contact Angles and the Adsorption of Liquids, Surface Phenomena Chem. Biol., Pergamon, 1958.
• [6] Y. S. Chow, Delayed sums and Borel summability of independent; identically distributed random variables, Bull. Inst. Math. Acad. Sinica 2 (1) (1973), pp. 207-220.
• [7] F. Dunlop and K. Topolski, Cassie’s law and convexity of wall tension with respect to disorder, J. Statist. Phys. 98 (5/6) (2000), pp. 1115-1124.
• [8] W. Feller, An Introduction to Probability Theory and Its Applications; I, Wiley, New York-London 1961.
• [9] J. Fröhlich and C. E. Pfister, The wetting and layering transitions in the half-infinite Ising model, Europhys. Lett. 3 (1987), pp. 845-852.
• [10] J. Fröhlich and C. E. Pfister, Semi-Infinite Ising model; I. Thermodynamic functions and phase diagram in absence of magnetic field, Comm. Math. Phys. 109 (1987), pp. 493-523.
• [11] P. G. de Gennes, Wetting: Statics and dynamics, Rev. Modern Phys. 57 (1985), pp. 827-870.
• [12] G. H. Hardy, Divergent Series, Clarendon Press, Oxford 1949.
• [13] D. Urban, K. Topolski and J. De Coninck, Wall tension and heterogeneous substrates, Phys. Rev. Lett. 76 (1996), pp. 4388-4391.