scholarly journals Geometry of the vacant set left by random walk on random graphs, Wright's constants, and critical random graphs with prescribed degrees

2020 ◽  
Vol 56 (3) ◽  
pp. 676-721
Author(s):  
Shankar Bhamidi ◽  
Sanchayan Sen
Keyword(s):  
Random Walk ◽  
Random Graphs ◽  
Critical Random Graphs

Critical random graphs and the structure of a minimum spanning tree

2008 ◽  
Vol 35 (3) ◽  
pp. 323-347 ◽  
Author(s):  
L. Addario-Berry ◽  
N. Broutin ◽  
B. Reed
Keyword(s):  
Random Graphs ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Critical Random Graphs

The continuum limit of critical random graphs

2010 ◽  
Vol 152 (3-4) ◽  
pp. 367-406 ◽  
Author(s):  
L. Addario-Berry ◽  
N. Broutin ◽  
C. Goldschmidt
Keyword(s):  
Random Graphs ◽  
Continuum Limit ◽  
Critical Random Graphs ◽  
The Continuum

A bernoulli excursion and its various applications

1991 ◽  
Vol 23 (03) ◽  
pp. 557-585 ◽  
Author(s):  
Lajos Takács
Keyword(s):  
Random Walk ◽  
Order Statistics ◽  
Asymptotic Distribution ◽  
Random Graphs ◽  
Random Variable ◽  
Random Walk Process

This paper is concerned with a random walk process in which and for i = 1, 2, ···, 2n . This process is called a Bernoulli excursion. The main object is to find the distribution, the moments, and the asymptotic distribution of the random variable ω n defined by . The results derived have various applications in the theory of probability, including random graphs, tournaments and order statistics.

scholarly journals Critical Random Graphs: Limiting Constructions and Distributional Properties

2010 ◽  
Vol 15 (0) ◽  
pp. 741-775 ◽  
Author(s):  
Louigi Addario-Berry ◽  
Nicolas Broutin ◽  
Christina Goldschmidt
Keyword(s):  
Random Graphs ◽  
Distributional Properties ◽  
Critical Random Graphs

scholarly journals Critical random graphs: Diameter and mixing time

2008 ◽  
Vol 36 (4) ◽  
pp. 1267-1286 ◽  
Author(s):  
Asaf Nachmias ◽  
Yuval Peres
Keyword(s):  
Random Graphs ◽  
Mixing Time ◽  
Critical Random Graphs
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