The diffusion limit for reversible jump processes on \(Z^ m\) with ergodic random bond conductivities. (English) Zbl 0523.60097


60K35 Interacting random processes; statistical mechanics type models; percolation theory
60J65 Brownian motion
Full Text: DOI


[1] Bensoussans, A., Lions, J. L., Papanicolaou, G.: Asymptotic analysis for periodic structures. Amsterdam: North Holland Publishing Company 1978 · Zbl 0404.35001
[2] Billingsley, P.: Convergence of probability measures. New York: J. Wiley & Sons 1968 · Zbl 0172.21201
[3] Breiman, L.: Probability. Reading: Addison Wesley 1968
[4] Chung, K. L.: Markov chains with stationary transition probabilities. Berlin: Springer 1960 · Zbl 0092.34304
[5] Donsker, M.: An invariance principle for certain probability limit theorems. Mem. Am. Math. Soc.6, 1951 · Zbl 0042.37602
[6] Kato, T.: Perturbation theory for linear operators, 2nd edn. Berlin: Springer 1976 · Zbl 0342.47009
[7] Kelley, J. L.: General topology. Princeton, New Jersey: Van Nostrand 1955 · Zbl 0066.16604
[8] Kirkpatrick, S.: Percolation and conduction, Rev. Mod. Phys.45, 574-588, 1973
[9] Kittel, Ch.: Introduction to solid state physics, 5th edn. New York: J. Wiley & Sons 1976
[10] Kurtz, T. G.: Approximation of population processes, Philadelphia: SIAM, 1981 · Zbl 0465.60078
[11] Lions, J. L.: Equations differentielles, operationelles. Berlin: Springer 1961
[12] Nash, J.: Continuity of solutions of parabolic and elliptic equations. Am. J. Math.80, 931-954, 1958 · Zbl 0096.06902
[13] Papanicolaou, G. C., Varadhan S. R. S.: Boundary value problems with rapidly oscillating random coefficients. Coll. Math. Soc. J?nos Bolyai, 27. Random Fields, Vol. 2, pp. 835-873, Amsterdam: North Holland Publ. Co. 1981
[14] Richtmyer, R. D.: Principles of advanced mathematical physics. New York: Springer 1978 · Zbl 0402.46001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.