Zobrazeno 1 - 10
of 109
pro vyhledávání: '"Kortchemski Igor"'
Publikováno v:
ESAIM: Proceedings and Surveys, Vol 74, Pp 19-37 (2023)
The first talk at the session Random trees and random forests “Journée MAS” (27/08/2021) was presented by I. Kortchemski. After a general up-to-date introduction to local and scaling limits of Bienaymé trees (which are discrete branching trees)
Externí odkaz:
https://doaj.org/article/7cc7b41e308f41839f23e1473d2d760d
Autor:
Kortchemski, Igor, Marzouk, Cyril
What is the analogue of L\'evy processes for random surfaces? Motivated by scaling limits of random planar maps in random geometry, we introduce and study L\'evy looptrees and L\'evy maps. They are defined using excursions of general L\'evy processes
Externí odkaz:
http://arxiv.org/abs/2402.04098
We establish lower tail bounds for the height, and upper tail bounds for the width, of critical size-conditioned Bienaym\'e trees. Our bounds are optimal at this level of generality. We also obtain precise asymptotics for offspring distributions with
Externí odkaz:
http://arxiv.org/abs/2311.06163
In the classical model of random recursive trees, trees are recursively built by attaching new vertices to old ones. What happens if vertices are allowed to freeze, in the sense that new vertices cannot be attached to already frozen ones? We are inte
Externí odkaz:
http://arxiv.org/abs/2308.00493
We investigate scaling limits of trees built by uniform attachment with freezing, which is a variant of the classical model of random recursive trees introduced in a companion paper. Here vertices are allowed to freeze, and arriving vertices cannot b
Externí odkaz:
http://arxiv.org/abs/2308.00484
Publikováno v:
ESAIM: Proceedings and Surveys, Vol 51, Pp 133-149 (2015)
This is a quick survey on some recent works done in the field of random maps, which, very roughly speaking, are graphs embedded without edge crossings in a surface. We present the main results and tools in this area then summarize the original cont
Externí odkaz:
https://doaj.org/article/52c263c2df464a03b006b75cb6275720
Autor:
Kortchemski, Igor, Thévenin, Paul
We construct a coupling between two seemingly very different constructions of the standard additive coalescent, which describes the evolution of masses merging pairwise at rates proportional to their sums. The first construction, due to Aldous \& Pit
Externí odkaz:
http://arxiv.org/abs/2301.01153
Publikováno v:
Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques, Tome 9 (2022), pp. 1305-1345
We investigate the structure of large uniform random maps with $n$ edges, $\mathrm{f}_n$ faces, and with genus $\mathrm{g}_n$ in the so-called sparse case, where the ratio between the number vertices and edges tends to $1$. We focus on two regimes: t
Externí odkaz:
http://arxiv.org/abs/2112.10719
Autor:
Kortchemski, Igor, Marzouk, Cyril
Publikováno v:
Ann. Appl. Probab. 33(5): 3755-3802 (October 2023)
We first establish new local limit estimates for the probability that a nondecreasing integer-valued random walk lies at time $n$ at an arbitrary value, encompassing in particular large deviation regimes. This enables us to derive scaling limits of s
Externí odkaz:
http://arxiv.org/abs/2101.01682
The genealogical structure of self-similar growth-fragmentations can be described in terms of a branching random walk. The so-called intrinsic area $\mathrm{A}$ arises in this setting as the terminal value of a remarkable additive martingale. Motivat
Externí odkaz:
http://arxiv.org/abs/1908.07830