Home | Contents | Submissions, editors, etc. | Login | Search | EJP
 Electronic Communications in Probability > Vol. 9 (2004) > Paper 20 open journal systems 


The Center of Mass of the ISE and the Wiener Index of Trees

Svante Janson, Uppsala University
Philippe Chassaing, Institut Elie Cartan


Abstract
We derive the distribution of the center of mass S of the integrated superBrownian excursion (ISE) from the asymptotic distribution of the Wiener index for simple trees. Equivalently, this is the distribution of the integral of a Brownian snake. A recursion formula for the moments and asymptotics for moments and tail probabilities are derived.


Full text: PDF

Pages: 178-187

Published on: December 30, 2004
Bibliography
  1. D. Aldous. Tree-based models for random distribution of mass. J. Statist. Phys. 73 (1993), 625-641. Math. Review 94k:60130
  2. D. Aldous. Brownian excursions, critical random graphs and the multiplicative coalescent. Ann. Probab. 25 (1997), 812-854. Math. Review 98d:60019
  3. J. Ambjorn, B. Durhuus, T. Jónsson. Quantum gravity, a statistical field theory approach. Cambridge Monographs on Mathematical Physics (1997) Cambridge University Press. Math. Review number not available.
  4. N.H. Bingham, C.M. Goldie, J.L. Teugels. Regular variation. Encyclopedia of Mathematics and its Applications 27 (1989) Cambridge University Press. Math. Review 90i:26003
  5. C. Borgs, J. Chayes, R. van der Hofstad, G. Slade. Mean-field lattice trees. On combinatorics and statistical mechanics. Ann. Comb. 3 (1999), 205-221. Math. Review 2001i:82036
  6. P. Chassaing, G. Schaeffer. Random planar lattices and integrated superBrownian excursion. Probab. Theory Related Fields 128 (2004), 161-212. Math. Review 2004k:60016
  7. L. Davies. Tail probabilities for positive random variables with entire characteristic functions of very regular growth. Z. Angew. Math. Mech. 56 (1976), T334-T336. Math. Review 0431331
  8. J.F. Delmas. Computation of moments for the length of the one dimensional ISE support. Electron. J. Probab. 8 (2003), 15 pp. . Math. Review 2041818
  9. A. Dembo, O. Zeitouni. Large deviations techniques and applications. Applications of Mathematics 38 (1998) Springer-Verlag. Math. Review 99d:60030
  10. A. Dembo, O. Zeitouni. Large deviations for random distribution of mass. Random discrete structures (Minneapolis, MN, 1993), 1989. IMA Vol. Math. Appl.76 (1996), 45-53. Math. Review 97d:60051
  11. E. Derbez, G. Slade. The scaling limit of lattice trees in high dimensions. Comm. Math. Phys. 193 (1998), 69-104. Math. Review 99b:60138
  12. S. Janson. The Wiener index of simply generated random trees. Random Structures Algorithms 22 (2003), 337-358. Math. Review 2004b:05186
  13. Y. Kasahara. Tauberian theorems of exponential type. J. Math. Kyoto Univ. 18 (1978), 209-219. Math. Review 80g:40008
  14. J.F. Le Gall. Spatial branching processes, random snakes and partial differential equations. Lectures in Mathematics ETH Zurich (1999) Birkhauser Verlag. Math. Review 2001g:60211
  15. J.F. Marckert, A. Mokkadem. States spaces of the snake and its tour-convergence of the discrete snake. J. Theoret. Probab. 16 (2003), 1015-1046. Math. Review 2033196
  16. L. Serlet. A large deviation principle for the Brownian snake. Stochastic Process. Appl. 67 (1997), 101-115. Math. Review 98j:60041
  17. G. Slade. Scaling limits and super-Brownian motion. Notices Amer. Math. Soc. 49 (2002), 1056-1067. Math. Review 2003g:60170
  18. J. Spencer. Enumerating graphs and Brownian motion. Comm. Pure Appl. Math. 50 (1997), 291-294. Math. Review 97k:05105
  19. E. M. Wright. The number of connected sparsely edged graphs. J. Graph Theory 1 (1977), 317-330. Math. Review 0463026
















Research
Support Tool
Capture Cite
View Metadata
Printer Friendly
Context
Author Address
Action
Email Author
Email Others


Home | Contents | Submissions, editors, etc. | Login | Search | EJP

Electronic Communications in Probability. ISSN: 1083-589X