Occupation statistics of critical branching random walks in two or higher dimensions

Annals of Probability

Volumn 39, Issue 1, 2011, Pages 327-368

  Lalley, Steven P ^a   Zheng, Xinghua ^b  

^a UNIVERSITY OF CHICAGO   (United States)

^b HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Hong Kong)

Author keywords

Critical branching random walks; Limit theorems; Occupation statistics

Indexed keywords

EID: 78650276017     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/10-AOP551     Document Type: Article

References (14)

1. ARONSON, D. G. and WEINBERGER, H. F. (1975). Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation. In Partial Differential Equations and Related Topics (Program, Tulane Univ., New Orleans, La., 1974). Lecture Notes in Math. 446 5-49. Springer, Berlin.
2. ATHREYA, K. B. and NEY, P. E. (1972). Branching Processes. Springer, New York.
3. BRAMSON, M., COX, J. T. and GREVEN, A. (1993). Ergodicity of critical spatial branching processes in low dimensions. Ann. Probab. 21 1946-1957.
4. ETHERIDGE, A. M. (2000). An Introduction to Superprocesses. University Lecture Series 20. Amer. Math. Soc., Providence, RI.
5. FLEISCHMAN, J. (1978). Limiting distributions for branching random fields. Trans. Amer. Math. Soc. 239 353-389.
6. GEIGER, J. (2000). A new proof of Yaglom's exponential limit law. In Mathematics and Computer Science (Versailles, 2000) 245-249. Birkhäuser, Basel.
7. LALLEY, S. P. (2009). Spatial epidemics: Critical behavior in one dimension. Probab. Theory Related Fields 144 429-469.
8. LAWLER, G. F. and LIMIC, V. (2010). Random Walk: A Modern Introduction. Cambridge Studies in Advanced Mathematics 123. Cambridge Univ. Press, Cambridge.
9. LYONS, R., PEMANTLE, R. and PERES, Y. (1995). Conceptual proofs of L log L ?criteria for mean behavior of branching processes. Ann. Probab. 23 1125-1138.
10. PERKINS, E. (1989). The Hausdorff measure of the closed support of super-Brownian motion. Ann. Inst. H. Poincaré Probab. Statist. 25 205-224.
11. PERKINS, E. A. (1988). A space-time property of a class of measure-valued branching diffusions. Trans. Amer. Math. Soc. 305 743-795.
12. RÉVÉSZ, P. (1994). Random Walks of Infinitely Many Particles. World Scientific, River Edge, NJ.
13. RÉVÉSZ, P. (1996). Distribution of the particles of a critical branching Wiener process. Bernoulli 2 63-80.
14. SPITZER, F. (1976). Principles of Random Walks, 2nd ed. Graduate Texts in Mathematics 34. Springer, New York.