no. 4
Conditioned brownian trees
Annales de l'I.H.P. Probabilités et statistiques, Tome 42 (2006) no. 4, pp. 455-489 
@article{AIHPB_2006__42_4_455_0,
     author = {Le Gall, Jean-Fran\c{c}ois and Weill, Mathilde},
     title = {Conditioned brownian trees},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {455--489},
     year = {2006},
     publisher = {Elsevier},
     volume = {42},
     number = {4},
     doi = {10.1016/j.anihpb.2005.08.001},
     mrnumber = {2242956},
     zbl = {1107.60053},
     language = {en},
     url = {https://www.numdam.org/articles/10.1016/j.anihpb.2005.08.001/}
}
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
SP  - 455
EP  - 489
VL  - 42
IS  - 4
PB  - Elsevier
UR  - https://www.numdam.org/articles/10.1016/j.anihpb.2005.08.001/
DO  - 10.1016/j.anihpb.2005.08.001
LA  - en
ID  - AIHPB_2006__42_4_455_0
ER  - 
%0 Journal Article
%A Le Gall, Jean-François
%A Weill, Mathilde
%T Conditioned brownian trees
%J Annales de l'I.H.P. Probabilités et statistiques
%D 2006
%P 455-489
%V 42
%N 4
%I Elsevier
%U https://www.numdam.org/articles/10.1016/j.anihpb.2005.08.001/
%R 10.1016/j.anihpb.2005.08.001
%G en
%F AIHPB_2006__42_4_455_0
Le Gall, Jean-François; Weill, Mathilde. Conditioned brownian trees. Annales de l'I.H.P. Probabilités et statistiques, Tome 42 (2006) no. 4, pp. 455-489. doi: 10.1016/j.anihpb.2005.08.001

[1] R. Abraham, W. Werner, Avoiding probabilities for Brownian snakes and super-Brownian motion, Electron. J. Probab. 2 (3) (1997) 27. | Zbl | MR

[2] R. Abraham, L. Serlet, Representations of the Brownian snake with drift, Stochastics Stochastics Rep. 73 (2002) 287-308. | Zbl | MR

[3] D. Aldous, The continuum random tree I, Ann. Probab. 19 (1991) 1-28. | Zbl | MR

[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. | Zbl | MR

[5] D. Aldous, The continuum random tree III, Ann. Probab. 21 (1993) 248-289. | Zbl | MR

[6] D. Aldous, Tree-based models for random distribution of mass, J. Statist. Phys. 73 (1993) 625-641. | Zbl | MR

[7] J. Bouttier, P. Di Francesco, E. Guitter, Random trees between two walls: exact partition function, J. Phys. A 36 (2003) 12349-12366. | Zbl | MR

[8] J. Bouttier, P. Di Francesco, E. Guitter, Statistics of planar graphs viewed from a vertex: a study via labeled trees, Nucl. Phys. B 675 (2003) 631-660. | Zbl | MR

[9] P. Chassaing, B. Durhuus, Statistical Hausdorff dimension of labelled trees and quadrangulations, Preprint, 2003.

[10] P. Chassaing, G. Schaeffer, Random planar lattices and integrated super-Brownian excursion, Probab. Theory Related Fields 128 (2004) 161-212. | Zbl | MR

[11] R. Cori, B. Vauquelin, Planar trees are well labeled trees, Canad. J. Math. 33 (1981) 1023-1042. | Zbl | MR

[12] J.F. Delmas, Computation of moments for the length of the one dimensional ISE support, Electron. J. Probab. 8 (17) (2003) 15. | Zbl | MR

[13] E. Derbez, G. Slade, The scaling limit of lattice trees in high dimensions, Comm. Math. Phys. 198 (1998) 69-104. | Zbl | MR

[14] T. Duquesne, A limit theorem for the contour process of conditioned Galton-Watson trees, Ann. Probab. 31 (2003) 996-1027. | Zbl | MR

[15] T. Duquesne, J.F. Le Gall, Probabilistic and fractal aspects of Lévy trees, Probab. Theory Related Fields 131 (2005) 553-603. | Zbl | MR

[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. | Zbl

[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. | Zbl | MR

[18] S. Janson, J.F. Marckert, Convergence of discrete snakes, J. Theoret. Probab. (2003), in press. | Zbl | MR

[19] K.M. Jansons, L.C.G. Rogers, Decomposing the branching Brownian path, Ann. Probab. 2 (1992) 973-986. | Zbl | MR

[20] O. Kallenberg, Random Measures, Academic Press, London, 1975. | Zbl | MR

[21] J.F. Le Gall, Brownian excursions, trees and measure-valued branching processes, Ann. Probab. 19 (1991) 1399-1439. | Zbl | MR

[22] J.F. Le Gall, The uniform random tree in a Brownian excursion, Probab. Theory Related Fields 96 (1993) 369-383. | Zbl | MR

[23] J.F. Le Gall, The Brownian snake and solutions of Δu=u 2 in a domain, Probab. Theory Related Fields 102 (1995) 393-432. | Zbl

[24] J.F. Le Gall, Spatial Branching Processes, Random Snakes and Partial Differential Equations, Lectures Math. ETH Zürich, Birkhäuser, Boston, 1999. | Zbl | MR

[25] J.F. Le Gall, A conditional limit theorem for tree-indexed random walk, Stochastic Process. Appl. (2005), in press. | Zbl | MR

[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. | Zbl | MR

[27] J.F. Marckert, A. Mokkadem, Limits of normalized quadrangulations. The Brownian map, Preprint, 2004. | MR

[28] D. Revuz, M. Yor, Continuous Martingales and Brownian Motion, Springer, Berlin, 1991. | Zbl | MR

[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. | Zbl | MR | Numdam

[30] W. Vervaat, A relation between Brownian bridge and Brownian excursion, Ann. Probab. 7 (1979) 143-149. | Zbl | MR

[31] M. Yor, Loi de l'indice du lacet brownien, et distribution de Hartman-Watson, Z. Wahr. Verw. Gebiete 53 (1980) 71-95. | Zbl | MR

Cité par Sources :