Compactness and fractal dimensions of inhomogeneous continuum random trees

被引：0

作者：

Blanc-Renaudie, Arthur ^{[1
]}

机构：

[1] Sorbonne Univ, Campus Pierre & Marie Curie,4 Pl Jussieu, F-75252 Paris 05, France

来源：

PROBABILITY THEORY AND RELATED FIELDS | 2023年 / 185卷 / 3-4期

关键词：

ICRT; Inhomogeneous continuum random trees; Compactness; Fractal dimensions; Stick breaking; Polya urn;

D O I：

10.1007/s00440-022-01138-9

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We introduce a new stick-breaking construction for inhomogeneous continuum random trees. This new construction allows us to prove the necessary and sufficient condition for compactness conjectured by Aldous et al. (Probab Theory Relat Fields 129(2):182-218, 2004) by comparison with Levy trees. We also compute the fractal dimensions (Minkowski, Packing, Hausdorff).

引用

页码：961 / 991

页数：31

共 50 条

[1] Compactness and fractal dimensions of inhomogeneous continuum random trees
Arthur Blanc-Renaudie
[J]. Probability Theory and Related Fields, 2023, 185 : 961 - 991
[2] Fractal dimensions and random walks on random trees
Konsowa, MH
Oraby, TF
[J]. JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 2003, 116 (02) : 333 - 342
[3] Stable trees as mixings of inhomogeneous continuum random trees
Wang, Minmin
[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2024, 175
[4] Fractal and resistance dimensions of random trees
Konsowa, Mokhtar H.
Al-Jarallah, Reem A.
[J]. PROBABILITY IN THE ENGINEERING AND INFORMATIONAL SCIENCES, 2007, 21 (04) : 623 - 634
[5] Cutting down p-trees and inhomogeneous continuum random trees
Broutin, Nicolas
Wang, Minmin
[J]. BERNOULLI, 2017, 23 (4A) : 2380 - 2433
[6] Inhomogeneous continuum random trees and the entrance boundary of the additive coalescent
David Aldous
Jim Pitman
[J]. Probability Theory and Related Fields, 2000, 118 : 455 - 482
[7] Inhomogeneous continuum random trees and the entrance boundary of the additive coalescent
Aldous, D
Pitman, J
[J]. PROBABILITY THEORY AND RELATED FIELDS, 2000, 118 (04) : 455 - 482
[8] LIMITS OF MULTIPLICATIVE INHOMOGENEOUS RANDOM GRAPHS AND LEVY TREES: THE CONTINUUM GRAPHS
Broutin, Nicolas
Duquesne, Thomas
Wang, Minmin
[J]. ANNALS OF APPLIED PROBABILITY, 2022, 32 (04): : 2448 - 2503
[9] The multiplicative coalescent, inhomogeneous continuum random trees, and new universality classes for critical random graphs
Shankar Bhamidi
Remco van der Hofstad
Sanchayan Sen
[J]. Probability Theory and Related Fields, 2018, 170 : 387 - 474
[10] Weak convergence of random p-mappings and the exploration process of inhomogeneous continuum random trees
David Aldous
Grégory Miermont
Jim Pitman
[J]. Probability Theory and Related Fields, 2005, 133 : 1 - 17

← 1 2 3 4 5 →