Scaling limits of multitype Bienaymé trees
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912511885836288 |
|---|---|
| author | Addario-Berry, Louigi Beltran, Philipp Stufler, Benedikt Thévenin, Paul |
| author_facet | Addario-Berry, Louigi Beltran, Philipp Stufler, Benedikt Thévenin, Paul |
| contents | We consider critical multitype Bienaymé trees that are either irreducible or possess a critical irreducible component with attached subcritical components. These trees are studied under two distinct conditioning frameworks: first, conditioning on the value of a linear combination of the numbers of vertices of given types; and second, conditioning on the precise number of vertices belonging to a selected subset of types. We prove that, under a finite exponential moment condition, the scaling limit as the tree size tends to infinity is given by the Brownian Continuum Random Tree. Additionally, we establish strong non-asymptotic tail bounds for the height of such trees. Our main tools include a flattening operation applied to multitype trees and sharp estimates regarding the structure of monotype trees with a given sequence of degrees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_23241 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Scaling limits of multitype Bienaymé trees Addario-Berry, Louigi Beltran, Philipp Stufler, Benedikt Thévenin, Paul Probability Combinatorics 60F17, 60C05 We consider critical multitype Bienaymé trees that are either irreducible or possess a critical irreducible component with attached subcritical components. These trees are studied under two distinct conditioning frameworks: first, conditioning on the value of a linear combination of the numbers of vertices of given types; and second, conditioning on the precise number of vertices belonging to a selected subset of types. We prove that, under a finite exponential moment condition, the scaling limit as the tree size tends to infinity is given by the Brownian Continuum Random Tree. Additionally, we establish strong non-asymptotic tail bounds for the height of such trees. Our main tools include a flattening operation applied to multitype trees and sharp estimates regarding the structure of monotype trees with a given sequence of degrees. |
| title | Scaling limits of multitype Bienaymé trees |
| topic | Probability Combinatorics 60F17, 60C05 |
| url | https://arxiv.org/abs/2507.23241 |