Fluctuation of the transition density for Brownian motion on random recursive Sierpinski gaskets

Stochastic Processes and their Applications

Volumn 92, Issue 1, 2001, Pages 61-85

  Hambly, B M ^a   Kumagai, Takashi ^b  

^a UNIVERSITY OF BRISTOL   (United Kingdom)

^b KYOTO UNIVERSITY   (Japan)

Author keywords

60J65; General branching process; Heat kernel; Laplace operator; Primary 60J60; Random recursive fractals; Resolvent density; Secondary 60J25

Indexed keywords

EID: 0002604957     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4149(00)00073-9     Document Type: Article

References (18)

1. Aronson D.G. Bounds on the fundamental solution of a parabolic equation. Bull. Amer. Math. Soc. 73:1967;890-896.
2. Barlow M.T. Diffusions on Fractals. Lectures on Probability Theory and Statistics: École d'été de probabilités de St Flour XXV. 1998;Springer, Berlin.
3. Barlow M.T., Hambly B.M. Transition density estimates for Brownian motion on scale irregular Sierpinski gaskets. Ann. Inst. H. Poincaré 33:1997;531-557.
4. Coulhon T., Grigoryan A. Random walks on graphs with regular volume growth. Geom. Funct. Anal. 8:1998;656-701.
5. Davies E.B. Heat Kernels and Spectral Theory. 1991;Cambridge University Press, Cambridge.
6. Falconer K.J. Random fractals. Math. Proc. Cambridge Philos. Soc. 100:1986;559-582.
7. Fitzsimmons P.J., Hambly B.M., Kumagai T. Transition density estimates for diffusion on affine nested fractals. Comm. Math. Phys. 165:1994;595-620.
8. Graf S. Statistically self-similar fractals. Probab. Theory Related Fields. 74:1987;357-392.
9. Hambly B.M. Brownian motion on a random recursive Sierpinski gasket. Ann. Probab. 25:1997;1059-1102.
10. Hambly B.M. On the asymptotics of the eigenvalue counting function for random recursive Sierpinski gaskets. Probab. Theory Related Fields. 117:2000;221-247.
11. Hambly, B.M., Jones, O.D., 2000. Thick and thin points for random recursive fractals. Preprint.
12. Hambly, B.M., Kigami J., Kumagai, T., 2000a. Multifractal formalisms for the local spectral and walk dimensions. Math. Proc. Cambridge Philos. Soc., to appear.
13. Hambly B.M., Kumagai T., Kusuoka S., Zhou X.Y. Transition density estimates for diffusion processes on homogeneous random Sierpinski carpets. J. Math. Soc. Japan. 52:2000;373-408.
14. Lindstrøm T. Brownian motion on nested fractals. Mem. Amer. Math. Soc. 420:1990.
15. Liu Q. The growth of an entire characteristic function and the tail probabilities of the limit of a tree martingale. Chauvin B.et al. Trees. Progress in Probability. Vol. 40:1996;51-80 Birkhauser, Basel.
16. Liu, Q., 1999. Local dimensions of the branching measure of a Galton-Watson tree. Preprint.
17. Mauldin R.D., Williams S.C. Random recursive constructions: asymptotic geometric and topological properties. Trans. Amer. Math. Soc. 295:1986;325-346.
18. Nerman O. On the convergence of supercritical general (C-M-J) branching processes. Z. Wahr. 57:1981;365-395.