scholarly journals On breadth‐first constructions of scaling limits of random graphs and random unicellular maps

2022 ◽  
Author(s):  
Grégory Miermont ◽  
Sanchayan Sen
Keyword(s):  
Random Graphs ◽  
Scaling Limits

scholarly journals Scaling Limits of Random Graphs from Subcritical Classes: Extended abstract

2015 ◽  
Vol DMTCS Proceedings, 27th... (Proceedings) ◽  
Author(s):  
Konstantinos Panagiotou ◽  
Benedikt Stufler ◽  
Kerstin Weller
Keyword(s):  
Random Graph ◽  
Random Graphs ◽  
Scaling Factor ◽  
Scaling Limits ◽  
First Passage Percolation ◽  
First Passage ◽  
Outerplanar Graphs ◽  
Nous Montrons ◽  
Analytic Expressions ◽  
International Audience

International audience We study the uniform random graph $\mathsf{C}_n$ with $n$ vertices drawn from a subcritical class of connected graphs. Our main result is that the rescaled graph $\mathsf{C}_n / \sqrt{n}$ converges to the Brownian Continuum Random Tree $\mathcal{T}_{\mathsf{e}}$ multiplied by a constant scaling factor that depends on the class under consideration. In addition, we provide subgaussian tail bounds for the diameter $\text{D}(\mathsf{C}_n)$ and height $\text{H}(\mathsf{C}_n^\bullet)$ of the rooted random graph $\mathsf{C}_n^\bullet$. We give analytic expressions for the scaling factor of several classes, including for example the prominent class of outerplanar graphs. Our methods also enable us to study first passage percolation on $\mathsf{C}_n$, where we show the convergence to $\mathcal{T}_{\mathsf{e}}$ under an appropriate rescaling. On s’int´eresse au comportement asymptotique du graphe aleatoire $\mathsf{C}_n$ sur $n$ sommets pris uniformément d’une classe sous-critique des graphes sur n sommets. Dans cette contribution nous montrons que le graphe normalisée$\mathsf{C}_n / \sqrt{n}$ converges vers un arbre aléatoire brownien continue Te multiplie par une constante qui dépends de la classede graphes considérée. Nous calculons l’expression analytique pour cette constante dans plusieurs cas parmi la classefameuse des graphes planaire extérieure. En plus, on montre que le diamètre $\text{D}(\mathsf{C}_n)$ et la hauteur $\text{H}(\mathsf{C}_n^\bullet)$ de l’équivalent racine de $\mathsf{C}_n$ sont bornes par des bornes sous gaussiens. Notre méthode nous permettons aussi de l’étudier la percolation du premier passage sur $\mathsf{C}_n$. Nous montrons que $\mathcal{T}_{\mathsf{e}}$ sujet a une changement d’échelle appropriée

scholarly journals Scaling Limits for Critical Inhomogeneous Random Graphs with Finite Third Moments

2010 ◽  
Vol 15 (0) ◽  
pp. 1682-1702 ◽  
Author(s):  
Shankar Bhamidi ◽  
Remco van der Hofstad ◽  
Johan van Leeuwaarden
Keyword(s):  
Random Graphs ◽  
Scaling Limits ◽  
Inhomogeneous Random Graphs

scholarly journals Scaling limits of random graphs from subcritical classes

2016 ◽  
Vol 44 (5) ◽  
pp. 3291-3334 ◽  
Author(s):  
Konstantinos Panagiotou ◽  
Benedikt Stufler ◽  
Kerstin Weller
Keyword(s):  
Random Graphs ◽  
Scaling Limits

scholarly journals Combinatorial approach to the interpolation method and scaling limits in sparse random graphs

2013 ◽  
Vol 41 (6) ◽  
pp. 4080-4115 ◽  
Author(s):  
Mohsen Bayati ◽  
David Gamarnik ◽  
Prasad Tetali
Keyword(s):  
Random Graphs ◽  
Interpolation Method ◽  
Scaling Limits ◽  
Combinatorial Approach

scholarly journals Novel scaling limits for critical inhomogeneous random graphs

2012 ◽  
Vol 40 (6) ◽  
pp. 2299-2361 ◽  
Author(s):  
Shankar Bhamidi ◽  
Remco van der Hofstad ◽  
Johan S. H. van Leeuwaarden
Keyword(s):  
Random Graphs ◽  
Scaling Limits ◽  
Inhomogeneous Random Graphs

Random Graphs

1998 ◽  
Author(s):  
V. F. Kolchin
Keyword(s):  
Random Graphs
Sign in / Sign up

Export Citation Format

Share Document