Conditioned brownian trees

Jean-François Le Gall; Mathilde Weill

Annales de l'I.H.P. Probabilités et statistiques (2006)

  • Volume: 42, Issue: 4, page 455-489
  • ISSN: 0246-0203

How to cite

top

Le Gall, Jean-François, and Weill, Mathilde. "Conditioned brownian trees." Annales de l'I.H.P. Probabilités et statistiques 42.4 (2006): 455-489. <http://eudml.org/doc/77903>.

@article{LeGall2006,
author = {Le Gall, Jean-François, Weill, Mathilde},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {random continuous tree; Brownian snake; Brownian excursion; integrated super-Brownian excursion; re-rooting},
language = {eng},
number = {4},
pages = {455-489},
publisher = {Elsevier},
title = {Conditioned brownian trees},
url = {http://eudml.org/doc/77903},
volume = {42},
year = {2006},
}

TY - JOUR
AU - Le Gall, Jean-François
AU - Weill, Mathilde
TI - Conditioned brownian trees
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2006
PB - Elsevier
VL - 42
IS - 4
SP - 455
EP - 489
LA - eng
KW - random continuous tree; Brownian snake; Brownian excursion; integrated super-Brownian excursion; re-rooting
UR - http://eudml.org/doc/77903
ER -

References

top
  1. [1] R. Abraham, W. Werner, Avoiding probabilities for Brownian snakes and super-Brownian motion, Electron. J. Probab.2 (3) (1997) 27. Zbl0890.60068MR1447333
  2. [2] R. Abraham, L. Serlet, Representations of the Brownian snake with drift, Stochastics Stochastics Rep.73 (2002) 287-308. Zbl1011.60055MR1932163
  3. [3] D. Aldous, The continuum random tree I, Ann. Probab.19 (1991) 1-28. Zbl0722.60013MR1085326
  4. [4] D. Aldous, The continuum random tree. II. An overview, in: Stochastic Analysis, Durham, 1990, London Math. Soc. Lecture Note Ser., vol. 167, Cambridge Univ. Press, Cambridge, 1991, pp. 23-70. Zbl0791.60008MR1166406
  5. [5] D. Aldous, The continuum random tree III, Ann. Probab.21 (1993) 248-289. Zbl0791.60009MR1207226
  6. [6] D. Aldous, Tree-based models for random distribution of mass, J. Statist. Phys.73 (1993) 625-641. Zbl1102.60318MR1251658
  7. [7] J. Bouttier, P. Di Francesco, E. Guitter, Random trees between two walls: exact partition function, J. Phys. A36 (2003) 12349-12366. Zbl1051.82010MR2025872
  8. [8] J. Bouttier, P. Di Francesco, E. Guitter, Statistics of planar graphs viewed from a vertex: a study via labeled trees, Nucl. Phys. B675 (2003) 631-660. Zbl1027.05021MR2018892
  9. [9] P. Chassaing, B. Durhuus, Statistical Hausdorff dimension of labelled trees and quadrangulations, Preprint, 2003. 
  10. [10] P. Chassaing, G. Schaeffer, Random planar lattices and integrated super-Brownian excursion, Probab. Theory Related Fields128 (2004) 161-212. Zbl1041.60008MR2031225
  11. [11] R. Cori, B. Vauquelin, Planar trees are well labeled trees, Canad. J. Math.33 (1981) 1023-1042. Zbl0415.05020MR638363
  12. [12] J.F. Delmas, Computation of moments for the length of the one dimensional ISE support, Electron. J. Probab.8 (17) (2003) 15. Zbl1064.60169MR2041818
  13. [13] E. Derbez, G. Slade, The scaling limit of lattice trees in high dimensions, Comm. Math. Phys.198 (1998) 69-104. Zbl0915.60076MR1620301
  14. [14] T. Duquesne, A limit theorem for the contour process of conditioned Galton–Watson trees, Ann. Probab.31 (2003) 996-1027. Zbl1025.60017MR1964956
  15. [15] T. Duquesne, J.F. Le Gall, Probabilistic and fractal aspects of Lévy trees, Probab. Theory Related Fields131 (2005) 553-603. Zbl1070.60076MR2147221
  16. [16] S.N. Evans, J.W. Pitman, A. Winter, Rayleigh processes, real trees and root growth with re-grafting, Probab. Theory Related Fields (2003), in press. Zbl1086.60050
  17. [17] T. Hara, G. Slade, The scaling limit of the incipient infinite cluster in high-dimensional percolation. II. Integrated super-Brownian excursion. Probabilistic techniques in equilibrium and nonequilibrium statistical physics, J. Math. Phys.41 (2000) 1244-1293. Zbl0977.82022MR1757958
  18. [18] S. Janson, J.F. Marckert, Convergence of discrete snakes, J. Theoret. Probab. (2003), in press. Zbl1084.60049MR2167644
  19. [19] K.M. Jansons, L.C.G. Rogers, Decomposing the branching Brownian path, Ann. Probab.2 (1992) 973-986. Zbl0771.60057MR1189426
  20. [20] O. Kallenberg, Random Measures, Academic Press, London, 1975. Zbl0345.60032MR818219
  21. [21] J.F. Le Gall, Brownian excursions, trees and measure-valued branching processes, Ann. Probab.19 (1991) 1399-1439. Zbl0753.60078MR1127710
  22. [22] J.F. Le Gall, The uniform random tree in a Brownian excursion, Probab. Theory Related Fields96 (1993) 369-383. Zbl0794.60080MR1231930
  23. [23] J.F. Le Gall, The Brownian snake and solutions of Δ u = u 2 in a domain, Probab. Theory Related Fields102 (1995) 393-432. Zbl0826.60062
  24. [24] J.F. Le Gall, Spatial Branching Processes, Random Snakes and Partial Differential Equations, Lectures Math. ETH Zürich, Birkhäuser, Boston, 1999. Zbl0938.60003MR1714707
  25. [25] J.F. Le Gall, A conditional limit theorem for tree-indexed random walk, Stochastic Process. Appl. (2005), in press. Zbl1093.60061MR2205115
  26. [26] J.F. Marckert, A. Mokkadem, State spaces of the snake and its tour – convergence of the discrete snake, J. Theoret. Probab.16 (2004) 1015-1046. Zbl1044.60083MR2033196
  27. [27] J.F. Marckert, A. Mokkadem, Limits of normalized quadrangulations. The Brownian map, Preprint, 2004. Zbl1117.60038MR2294979
  28. [28] D. Revuz, M. Yor, Continuous Martingales and Brownian Motion, Springer, Berlin, 1991. Zbl0731.60002MR1083357
  29. [29] R. van der Hofstad, G. Slade, Convergence of critical oriented percolation to super-Brownian motion above 4 + 1 dimensions, Ann. Inst. H. Poincaré Probab. Statist.39 (2003) 413-485. Zbl1020.60099MR1978987
  30. [30] W. Vervaat, A relation between Brownian bridge and Brownian excursion, Ann. Probab.7 (1979) 143-149. Zbl0392.60058MR515820
  31. [31] M. Yor, Loi de l'indice du lacet brownien, et distribution de Hartman–Watson, Z. Wahr. Verw. Gebiete53 (1980) 71-95. Zbl0436.60057MR576898

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.