Abstract
This is a note on a local ergodic theorem for a symmetric exclusion process defined on an infinite tower of coverings, which is associated with a finitely generated residually finite amenable group.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bartholdi, L., Grigorchuk, R., Nekrashevych, V.: From fractal groups to fractal sets. In: Fractals in Graz 2001. Trends Mathematics, pp. 25–118. Birkhäuser, Basel (2003)
Bartholdi, L., Virág, B.: Amenability via random walks. Duke Math. J. 130 (1), 39–56 (2005)
Ceccherini-Silberstein, T., Coornaert, M.: Cellular Automata and Groups. Springer Monographs in Mathematics. Springer-Verlag, Berlin (2010)
Funaki, T., Handa, K., Uchiyama, K.: Hydrodynamic limit of one-dimensional exclusion processes with speed change. Ann. Probab. 19 (1), 245–265 (1991)
Guo, M.Z., Papanicolaou, G.C., Varadhan, S.R.S.: Nonlinear diffusion limit for a system with nearest neighbor interactions. Comm. Math. Phys. 118 (1), 31–59 (1988)
Jara, M.: Hydrodynamic limit for a zero-range process in the Sierpinski gasket. Comm. Math. Phys. 288 (2), 773–797 (2009)
Kaimanovich, V.A.: Random walks on Sierpiński graphs: hyperbolicity and stochastic homogenization. In: Fractals in Graz 2001. Trends Mathematics, pp. 145–183. Birkhäuser, Basel (2003)
Kipnis, C., Landim, C.: Scaling Limits of Interacting Particle Systems. Grundlehren der Mathematischen Wissenschaften, vol. 320. Springer, Berlin (1999)
Kipnis, C., Landim, C., Olla, S.: Hydrodynamical limit for a nongradient system: the generalized symmetric exclusion process. Comm. Pure Appl. Math. 47 (11), 1475–1545 (1994)
Kipnis, C., Olla, S., Varadhan, S.R.S.: Hydrodynamics and large deviation for simple exclusion processes. Comm. Pure Appl. Math. 42 (2), 115–137 (1989)
Kotani, M., Sunada, T.: Albanese maps and off diagonal long time asymptotics for the heat kernel. Comm. Math. Phys. 209 (3), 633–670 (2000)
Nekrashevych, V.: Self-Similar Groups. Mathematical Surveys and Monographs, vol. 117. American Mathematical Society, Providence (2005)
Olla, S., Sasada, M.: Macroscopic energy diffusion for a chain of anharmonic oscillators. Probab. Theory Relat. Fields 157 (3–4), 721–775 (2013)
Sasada, M.: Spectral gap for stochastic energy exchange model with nonuniformly positive rate function. Ann. Probab. 43 (4), 1663–1711 (2015)
Sasada, M., Kametani, Y.: A new technique for the computation of central limit theorem variances for exclusion processes and its application. Talk at Research Institute for Mathematical Sciences, Kyoto University (2015)
Spohn, H.: Large Scale Dynamics of Interacting Particles. Texts and Monograph in Physics. Springer-Verlag, Heidelberg (1991)
Tanaka, R.: Hydrodynamic limit for weakly asymmetric simple exclusion processes in crystal lattices. Comm. Math. Phys. 315 (3), 603–641 (2012)
Acknowledgements
The author thanks Hiroshi Kawabi for helpful comments and encouragement, Motoko Kotani for support during this work and an anonymous referee for useful comments to improve this note.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer Japan
About this paper
Cite this paper
Tanaka, R. (2016). A Note on a Local Ergodic Theorem for an Infinite Tower of Coverings. In: Nishiura, Y., Kotani, M. (eds) Mathematical Challenges in a New Phase of Materials Science. Springer Proceedings in Mathematics & Statistics, vol 166. Springer, Tokyo. https://doi.org/10.1007/978-4-431-56104-0_6
Download citation
DOI: https://doi.org/10.1007/978-4-431-56104-0_6
Published:
Publisher Name: Springer, Tokyo
Print ISBN: 978-4-431-56102-6
Online ISBN: 978-4-431-56104-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)