Locally Perturbed Random Walks with Unbounded Jumps

Preprint English OPEN
Paulin, Daniel; Szász, Domokos;
(2010)

In \cite{SzT}, D. Sz\'asz and A. Telcs have shown that for the diffusively scaled, simple symmetric random walk, weak convergence to the Brownian motion holds even in the case of local impurities if $d \ge 2$. The extension of their result to finite range random walks i... View more
  • References (20)
    20 references, page 1 of 2

    1. Bleher, P. M.: Statistical Properties of Two-Dimensional Periodic Lorentz Gas with Infinite Horizon. J. of Stat. Physics, 66(1):315-373, 1992.

    2. Chernov, N. and Dolgopyat, D.: Hyperbolic billiards and statistical physics Proc. of International Congress of Mathematicians (Madrid, Spain, August 2006), Vol. II, Euro. Math. Soc., Zurich, 2006, pp. 1679-1704.

    3. Chernov, N., and Dolgopyat, D.: Anomalous current in periodic Lorentz gases with infinite horizon, Uspekhi Mat. Nauk, 64:4 (2009), 73-124 (in Russian), Russ. Math. Surveys, 64 (2009) 651-699

    4. Chernov, N., and Dolgopyat, D.: Lorentz gas with thermostatted walls, pp. 50, submitted

    5. Dolgopyat, D., Szász, D. and Varjú, T.: Limit Theorems for Locally Perturbed Planar Lorentz Processes, Duke Math. Journal, 148: 459-499, 2009

    6. Dvoretzky, A. and Erdős, P.: Some problems on random walk in space. Proc. 2nd Berkeley Sympos. Math. Statis. Probab., pp. 353-367 (1951)

    7. Gnedenko, B.V. and Kolmogorov, A.N.: Limit distributions for sums of independent random variables. Revised Edition (1968), Translated by K.L.Chung. Afterword: J. L. Doob. Addison-Wesley series in statistics. ASIN: B000WSX412

    8. Harrison, J. M. and Shepp, L. A. On Skew Brownian Motion Ann. Probab. Volume 9, Number 2 (1981), 309-313.

    9. Ibragimov, I. A. and Linnik, Yu. V.: Independent and Stationary Sequences of Random Variables 1971 Wolters-Noordhoff Publishing Groningen

    10. Lawler, G. F. and Limic, V.: Random walk: a modern introduction. To be published by Cambridge University Press. Electronic version available at http://www.math.uchicago.edu/∼lawler/srwbook.pdf.

  • Metrics
Share - Bookmark