Jun 7 – 10, 2021
En Ligne
Europe/Paris timezone

Asymptotic probability of connected labeled objects and virtual species

Jun 8, 2021, 4:20 PM
25m
En Ligne

En Ligne

https://greenlight.lal.cloud.math.cnrs.fr/b/oli-yhz-7hx

Speaker

Khaydar Nurligareev (Université Paris 13)

Description

There are a number of combinatorial structures that admit a notion of connectivity, including graphs
as the most commonly used example. We are interested in the probability that a random labeled object
is connected, as its size tends to in?nity. We will show that the asymptotics for these probabilities can
be obtained in a common manner and that asymptotic coe?cients have a combinatorial meaning in terms
of virtual species. Moreover, we will show how to get the asymptotic probability that a random labeled
object has a given number of connected components, and we will indicate the combinatorial meaning of the
coe?cients involved in the asymptotic expansions.
This is ongoing work joint with Thierry Monteil.

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