Zobrazeno 1 - 10
of 919
pro vyhledávání: '"Chapuy, P."'
Autor:
Chapuy, Guillaume
We consider a Tamari interval of size $n$ (i.e., a pair of Dyck paths which are comparable for the Tamari relation) chosen uniformly at random. We show that the height of a uniformly chosen vertex on the upper or lower path scales as $n^{3/4}$, and h
Externí odkaz:
http://arxiv.org/abs/2403.18719
We prove that uniform random triangulations whose genus is proportional to their size $n$ have diameter of order $\log n$ with high probability. We also show that in such triangulations, the distances between most pairs of points differ by at most an
Externí odkaz:
http://arxiv.org/abs/2311.04005
Autor:
Chapuy, Guillaume, Perarnau, Guillem
We give a short proof of the fact that the number of labelled trees on $n$ vertices is $n^{n-2}$. Although many short proofs are known, we have not seen this one before.
Comment: 2 pages
Comment: 2 pages
Externí odkaz:
http://arxiv.org/abs/2306.12918
Autor:
Chapuy, Guillaume
Bassino et al. (arXiv:1907.08517) have shown that uniform random co-graphs (graphs without induced $P_4$) of size $n$ converge to a certain non-deterministic graphon. The edge-density of this graphon is a random variable $\Lambda \in [0,1]$ whose fir
Externí odkaz:
http://arxiv.org/abs/2306.07911
Autor:
Matthias Münchhalfen, Richard Görg, Michael Haberl, Jens Löber, Jakob Willenbrink, Laura Schwarzt, Charlotte Höltermann, Christian Ickes, Leonard Hammermann, Jan Kus, Björn Chapuy, Andrea Ballabio, Sybille D. Reichardt, Alexander Flügel, Niklas Engels, Jürgen Wienands
Publikováno v:
Nature Communications, Vol 15, Iss 1, Pp 1-21 (2024)
Abstract Ligation of the B cell antigen receptor (BCR) initiates humoral immunity. However, BCR signaling without appropriate co-stimulation commits B cells to death rather than to differentiation into immune effector cells. How BCR activation deplet
Externí odkaz:
https://doaj.org/article/d3d3f15046064c9eadb2e5e5e120d8db
The integrated super-Brownian excursion (ISE) is the occupation measure of the spatial component of the head of the Brownian snake with lifetime process the normalized Brownian excursion. It is a random probability measure on $\mathbb{R}$, and it is
Externí odkaz:
http://arxiv.org/abs/2210.10159
Autor:
Chapuy, Guillaume, Perarnau, Guillem
We prove that a uniformly random automaton with $n$ states on a 2-letter alphabet has a synchronizing word of length $O(n^{1/2}\log n)$ with high probability (w.h.p.). That is to say, w.h.p. there exists a word $\omega$ of such length, and a state $v
Externí odkaz:
http://arxiv.org/abs/2207.14108
We study the correlators $W_{g,n}$ arising from Orlov-Scherbin 2-Toda tau functions with rational content-weight $G(z)$, at arbitrary values of the two sets of time parameters. Combinatorially, they correspond to generating functions of weighted Hurw
Externí odkaz:
http://arxiv.org/abs/2206.14768
Publikováno v:
Ann. Probab. 52 (4), 1253-1359, (July 2024)
We study the asymptotic behaviour of random integer partitions under a new probability law that we introduce, the Plancherel-Hurwitz measure. This distribution, which has a natural definition in terms of Young tableaux, is a deformation of the classi
Externí odkaz:
http://arxiv.org/abs/2206.11315
Publikováno v:
Algebraic Combinatorics, Volume 5 (2022) no. 6, pp. 1363-1390
In this note, we examine how the BKP structure of the generating series of several models of maps on non-oriented surfaces can be used to obtain explicit and/or efficient recurrence formulas for their enumeration according to the genus and size param
Externí odkaz:
http://arxiv.org/abs/2110.12834