The existence of a steady state for perturbed symmetric random walk on a random lattice

• Autorzy: Komorowski T. , Krupa G.
• Języki publikacji: EN

Abstrakty

EN

In the present paper we consider a continuous time random walk on an anisotropic random lattice. We show the existence of a steady state ̄μ_α for the environment process (ζ(t))_{t ≥ 0} corresponding to the walk. This steady state has the property that the ergodic averages of (F(ζ(t)))_{t ≥ 0}, where F is local (i.e. it depends on finitely many bonds of the lattice only), converge almost surely in the annealed measure to ∫Fd ̄μ_α.

Słowa kluczowe

EN

random field; passive tracer; random walk in random environment; Einstein relation

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2004
• Tom: Vol. 24, Fasc. 1
• Strony: 121--144
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Komorowski T.

• Institute of Mathematics, UMCS, pl. Marii Curie-Skłodowskiej 1, Lublin 20-031, Poland

autor

Krupa G.

• The Catholic University of Lublin, Faculty of Mathematics and Natural Science, Lublin, Poland

Bibliografia

• [1] N. Dunford and J. T. Schwartz, Linear Operators. I, Wiley, New York 1988.
• [2] G. M. Fichtenholtz, A Course of Differential and Integral Calculus, Vol. 2 (in Russian), Fizmatgiz, Moscow 1959.
• [3] S. Havlin and A. Bunde, Transport in the presence of additional physical constraints, in: Fractals and Disordered Systems, A. Bunde and S. Havlin (Eds.), Springer, 1991.
• [4] C. Kipnis and C. Landim, Scaling Limits of lnteracting Particle Systems, Springer, Berlin 1999.
• [5] T. Komorowski and G. Krupa, On stationarity of Lagrangian observations of passive tracer velocity in a compressible environment, Ann. Appl. Probab. (2003), to appear.
• [6] T. Komorowski and S. Olla, Einstein relation for random walks on a lattice with random bonds, preprint.
• [7] A. Lasota and M. Mackey, Probabilistic Properties of Deterministic Systems, Cambridge Univ. Press, 1985.
• [8] T. M. Liggett, Stochastic Interacting Systems, Springer, New York-Berlin 1999.
• [9] L. Shen, Asymptotic properties of anisotropic walks in random media, Ann. Appl. Probab. 9 (2002), pp. 477-510.
• [10] A. S. Sznitman and M. Zerner, A law of large numbers for random walks in random environment, Ann. Probab. 27 (1999), pp. 1851-1869.