Ergodicity of avalanche transformations
Dynamical Systems: An International Journal
Taylor & Francis
© 2014 Taylor & Francis. This is the author's accepted manuscript. The final version is available from Taylor & Francis via the DOI in this record.
In this paper, we study dynamical systems of product type and some particular inducing scheme motivated by neural dynamics (called avalanche transformation). We derive the distribution of avalanche sizes and give sufficient conditions such that the avalanche transformation is ergodic. Moreover, we deduce a multivariate central limit theorem as a corollary.
We would like to thank Ira Gessel and Wlodek Bryc for some helpful remarks concerning Section 2. The research of M. Denker was supported by the National Science Foundation grant DMS- 1008538. The research of A. Rodrigues is supported by the Swedish Research Council (VR Grant 2010/5905). The authors would like to thank the Goran Gustafsson Foundation UU/KTH for the ¨ financial support.
Vol. 29, No. 4, pp. 517-536