Fluctuations of principal eigenvalues and random scales

Communications in Mathematical Physics

Volumn 189, Issue 2, 1997, Pages 337-363

  Sznitman, Alain Sol ^a  

^a ETH ZURICH   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039270172     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200050206     Document Type: Article

References (19)

1. Albeverio, S., Molchanov, S.A., Surgailis, D.: Stratified structure of the universe and Burger's equation - A probabilistic approach. Probab. Th. Rel. Fields 100, 457-484 (1994)
2. Beliaev, A.Yu., Yurinsky, V.V.: The spectrum bottom of the Laplacian in a Poisson cloud. Siberian Adv. in Math. 5, No. 4, 113-150 (1995)
3. Bolthausen, E.: Localization of a two-dimensional random walk with an attractive path interaction. Ann. Probab. 22, 875-918 (1994)
4. Burago, Yu.D., Zalgaller, V.A.: Geometric inequalities. Berlin: Springer-Verlag, 1988
5. Chavel, I: Eigenvalues in Riemannian geometry: New York: Academic Press, 1984
6. Dobrushin, R.L., Kotecky, R., Shlosman, S.: Wulff construction: A global shape from local interaction. AMS Translations series 104, Providence R.I. Am. Math. Soc., 1992
7. Fukushima, M.: it Dirichlet forms and Markov processes. Kodansha, Amsterdam, Tokyo: North-Holland, 1980
8. Hall, P.: Distribution of size, structure and number of vacant regions in a high intensity mosaic. Z. f. Wahrsch. verw. Gebiete 70, 237-261 (1985)
9. Hall, R.R.: A quantitative isoperimetric inequality in n-dimensional space. J. reine angew. Math. 428, 161-176
10. c for the Ising model in two dimensions. Probab. Th. Rel. Fields 102, 3, 313-330 (1995)
11. Janson, S.: Bounds on the distribution of extremal values of a scanning process. Stoch. Proc. and their Appl. 18, 313-328 (1984)
12. Janson, S.: Random coverings in several dimensions. Acta Math. 156, 83-118 (1986)
13. Krug, J., Halpin Healy, T.: Directed polymer in the presence of columnar disorder. J. Phys. I, France, 3, 2179-2198 (1993)
14. Melas, A.D.: The stability of some eigenvalue estimates. J. Differential Geometry 36, 19-33 (1992)
15. Osserman, R.: Bonnesen-style isoperimetric inequalities. Amer. Math. Monthly 86, 1-29 (1979)
16. Sznitman, A.S.: On the confinement property of Brownian motion among Poissonian obstacles. Comm. Pure Appl. Math. 44, 1137-1170 (1991)
17. Sznitman, A.S.: Brownian confinement and pinning in a Poissonian potential I, II. Probab. Th. Rel. Fields 105, 1-30, 31-56 (1996)
18. Sznitman, A.S.: Capacity and principal eigenvalues: The method of enlargement of obstacles revisited. Ann. Probab. 25, 3, 1180-1209 (1997)
19. Tsuji, M.: Potential theory in modern function theory. 2nd ed., New York: Chelsea, 1975